Seminars

Math-Fi seminar on 5 June. (Co-organized as a Quantum Walk Seminar)

2025.06.03 Tue up
Math-Fi seminar on 5 June. (Co-organized as a Quantum Walk Seminar)
Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
Time: 15:40–19:00
 
  • Speaker 1: Ryoichi Suzuki (Tokyo University of Science)
  • Time: 15:40–16:40
  • Title: Malliavin-Mancino-Taylor type formulas and their applications to finance
  • Abstract: 
This presentation briefly introduces the Clark-Ocone-Haussmann (COH) formula, providing a martingale representation of random variables, and its Taylor-type extension, the Malliavin-Mancino-Taylor (MMT) formula. We then focus on developing MMT type formulas formulas for jump processes, specifically for $L^1$and $L^2$-pure jump additive processes, including versions under a change of measure. A key application is the derivation of explicit risk-minimizing hedging strategies in financial market models driven by pure jump additive processes. 
These results, from joint work by M. Handa, M.E. Mancino, advance Malliavin calculus tools for finance.
 
  • Speaker 2: Johannes Ruf (London School of Economics)
  • Time: 16:50-17:50
  • Title: Predictable variations in stochastic calculus
  • Abstract: 
The focus of this talk is the transformation of increments of a stochastic process by a predictable function. Many operations in stochastic analysis can be considered under this point of view. Stochastic integrals, for example, are linear functionals of process increments.  Although mathematically equivalent, focusing on transformation of increments often leads to simpler proofs of more general statements in stochastic calculus. In this talk specifically, we illustrate how considering predictable variations lead to various Ito-type formulas.
Joint work with Ales Cerny
 
  • Speaker 3: Tomoyuki Terada（Kanazawa Institute of Technology）
  • Time: 18:00-19:00
  • Title: Szegedy walkの確率測度と再帰性に関する最近の研究
  • Abstract: 
量子ウォークの挙動を明らかにする上で、ウォーカーの確率測度を明示的に求めることは、基本的かつ重要な問題である。本講演では、パスグラフ上のSzegedy walkに対するスペクトル解析を通じて、この確率測度を導出する手法を紹介する（今野・井手・寺田, 2023,YMJ）。具体的には、パスグラフ上のランダムウォークから誘導されるヤコビ行列の固有値および固有ベクトルを用いて、確率測度の公式を得る。パスグラフ上のランダムウォークでは、直交多項式の性質を活用し、Karlin–McGregorの公式によって確率測度が具体的に記述されることが知られているが、本研究はこれに対応する量子ウォークの結果とも言える。また、ランダムウォークおよび量子ウォークにおける再帰確率に関する最近の話題についても紹介する。

Math-Fi seminar on 29 May.

2025.05.29 Thu up
  • Date: 29 May. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–18:20 
  • Speaker : Hau-Tieng Wu (New York University, Courant)
  • Title: Quantifying Uncertainty in Time-Frequency Analysis under Nonstationary Noise
  • Abstract: 
Time-frequency (TF) analysis provides a flexible framework for studying nonstationary time series, with wide applications across the sciences and engineering. Yet in real-world data, noise is ubiquitous and often nonstationary, and our ability to quantify uncertainty in TF representations remains limited. In this talk, we present recent progress on understanding and addressing this challenge. We show that the short-time Fourier transform (STFT) of a broad class of nonstationary noise processes that is defined via filtrations satisfying mild moment and dependence conditions can be approximated in L2 by a Gaussian process. This result arises from a sequential Gaussian approximation theorem, which may be of independent interest. In the presence of signal (the nonnull setup), we prove that the reconstruction formula underlying the synchrosqueezing transform (SST) remains stable under such noise, with uniform error bounds. When the noise satisfies a stronger local stationarity property, we develop a bootstrap procedure with theoretical guarantee to quantify uncertainty in both the STFT and SST, which relies on a time-varying autoregressive approximation of the noise. We conclude by demonstrating the practical value of this framework through an application to airflow signals recorded during sleep.

Math-Fi seminar on 22 May. (Co-organized as a Quantum Walk Seminar)

2025.05.20 Tue up
  • Date: 22 May. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–19:00
 
  • Speaker 1: Ryuya Namba（Kyoto Sangyo University）
  • Time: 16:50-17:50
  • Title: 多重ゼータ関数と高次元ランダムウォーク
  • Abstract: 
一般にある多変数関数が特性関数となるか否かを判別することは, 対応する測度が高次元離散型確率分布となることが自明でない場合には難しいことが知られている. 本講演ではd次元整数格子上に有限個の点, または可算無限個の点に重みをもつ高次元離散型分布及びその畳込により得られるランダムウォークを多重ゼータ関数及び多変数Eule 積を用いて表記する. 特に後者の場合に, 対応する特性関数が無限分解可能となるための簡易な十分条件を与える.
 
 
  • Speaker 2: Satoshi Watanabe（KDDI Research, Inc.）
  • Time: 18:00–19:00
  • Title: Lackadaisical quantum walkによる頂点探索
  • Abstract: 
quantum walkは頂点グラフの目標点(marked points)を探索する際に用いられる。このquantum walkでself loopを加えたものをlackadaisical quantum walkと呼び、探索の成功確率の向上や探索の高速化に用いられてきた。
　ここで頂点グラフに置いて、従来のコイン作用素では探索できないような例外的な配置が存在する。例えば2次元の周期境界条件を課した格子において、隣接した2点がmarked pointsの場合、対角線上にmarked pointsが並んだ場合などは例外的な配置に相当し、従来のGrover walkやlackadaisical quantum walkでは探索できないような配置になっている。
　本発表ではlackadaisical quantum walkのコイン演算子を変形した新たなコインを導入することによって頂点グラフにおける様々な例外的配置を探索できることを紹介する。また他のコインでは例外的な配置を探索できないことをquantum walkの定常状態を構成することによって理論的に示せるということを紹介する。発表に置いては今回新たに研究した2次元の周期境界条件を課した格子にHanoi型のlong edgeを付け加えたグラフについての結果を紹介する。本研究はGiri Ranjan Pulak氏(株式会社KDDI総合研究所)との共同研究に基づいている。

Math-Fi seminar on 15 May.

2025.05.13 Tue up
  • Date: 15 May. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time:  16:50–19:00
     
  • Speaker 1: Ju-Yi Yen (University of Cincinnatti)
  • Time: 16:50–17:50
  • Title: Excursion-Theoretic Approaches to Limit Theorems for Additive Functionals of Markov Processe
  • Abstract:
This talk explores a uni ed excursion-theoretic framework for proving limit theorems of additive functionals associated with various classes of Markov processes, including Brownian motion, null recurrent di usions, and symmetric strong Markov processes. Motivated by classical results such as the Darling Kac theorem and the Ray Knight theorems, we investigate how local time provides a natural time scale for analyzing functionals of processes that do not admit nite invariant measures. We begin with Brownian motion, where the inverse local time at zero enables a strong law of large numbers and central limit theorem for time integrals of functions along sample paths. These results are revisited using Itos excursion theory, highlighting its utility in both deriving moments and capturing uctuation behavior. We then extend these ideas to null recurrent linear di usions by transforming them into time-changed Brownian motions via Zvonkins method. Excursion-based representations again yield central limit theorems, even in the absence of stationary distributions. Finally, we examine a broader setting of symmetric strong Markov processes, where local times are used to de ne regenerative structures. By leveraging generalized RayKnight theorems and Gaussian process techniques, we establish limit theorems under minimal assumptions, unifying previous results under a single probabilistic strategy. This excursion-centric viewpoint not only clari es asymptotic behaviors but also opens paths toward analyzing more complex dynamics such as complex-valued processes and higher-dimensional extensions.

 
  • Speaker 2: Loïc Chaumont (Université d’Angers)
  • Time: 18:00–19:00
  • Title: Levy processes resurrected in the positive half-line
  • Abstract:
Levy processes resurrected in the positive half-line is a Markov process obtained by removing successively all jumps that make it negative. A natural question, given this construction, is whether the resulting process is absorbed at 0 or not. In this work, we give conditions for absorption and conditions for non absorption bearing on the characteristics of the initial Levy process. First, we shall give a detailed definition of the resurrected process whose law is described in terms of that of the process killed when it reaches the negative half line. In particular, we will specify the explicit form of the resurrection kernel. Then we will see that when the initial Levy process X creeps downward and satisfies certain additional condition, the resurrected process is absorbed at 0 with probability one, independently of its starting
point. Some criteria for absorption and some criteria for non absorption will be given. The most delicate case is when X enters immediately in the negative half line and drifts to -infinity. It is then possible to give a sufficient condition for absorption but up to now, even when X is the negative of a subordinator, we do not know whether this condition can be dropped or not. We shall take a closer look at the case of stable processes. This is a joint work with Victor Rivero (CIMAT, Guanajuato) and Marria Emilia Caballero (Instituto de Matematicas, UNAM, Mexico).
 

Math-Fi seminar on 24 Apr.

2025.04.22 Tue up
  • Date: 24 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 13:10–19:00


  • Speaker 1: Dima Ivanenko (Taras Shevchenko National University of Kyiv)
  • Time: 13:10–14:10
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES <4>
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.
 
 
  • Speaker 2: Oleksii Kulik　 (Wroclaw University of Science and Technology)
  • Time: 14:20-15:20
  • Title: A moments respecting explicit simulation scheme for L´evy driven SDEs, II: Simulation methods for SDEs with super-linearly dissipative drifts.
  • Abstract:
This is the first of two lectures devoted to the effect of tails/moments transformation by a dissipative drift for  solutions of SDEs driven by heavy-tailed noises.  In the first lecture we will discuss the history of the subject, illustrate how does this effect reveals itself in various settings, and provide a complete description of the effect in a general semi-martingale setting.
 
 
  • Speaker 3: Maria Elvira Mancino (University of Florence)
  • Time: 16:50-17:50
  • Title: Asymptotic Efficiency of the Fourier Spot Volatility Estimator with Noisy Data and an Application to the estimation of spot Beta and higher-order spot covariances.
  • Abstract:
We study the efficiency and robustness of the Fourier spot volatility estimator when high-frequency prices are contaminated by microstructure noise. Firstly, we show that the estimator is consistent and asymptotically efficient in  the presence of additive noise, establishing a Central Limit Theorem with the optimal rate of convergence 1/8. Feasible CLTs with the optimal convergence rate are also obtained, by proving the consistency of the Fourier estimators of the spot volatility of volatility and the quarticity in the presence of noise. The multivariate case is also studied.
Finally, we exploit this methodology to introduce a consistent estimator of the spot asset beta. We provide simulation results that suggest that our spot beta estimator has a robust finite-sample performance in the presence of realistic market features such as rough volatility, inhomogeneous asynchronous sampling, autocorrelated and price-dependent noise and price rounding. Additionally, we conduct an empirical study with tick-by-tick prices in which we reconstruct intraday spot beta paths.
 
 
  • Speaker 4: Shigeki Matsutani（Kanazawa University）
  • Time: 18:00-19:00
  • Title: 量子ウォークと光学
  • Abstract:
本講演では，一次元量子ウォークと光学におけるS行列理論との関連を示す．
光学における転送行列理論は，一次元のHermholz方程式を離散化することで得られる．
この転送行列の系を入射光と出射光で再定式化すると，S行列（散乱行列）が得られる．
さらに，入射光から出射光への静的な変換を，因果関係あるいは一種の離散的時間発展として動的な波動系を考えると，1次元量子ウォークと一致する．
産業界における光学現象には，波動系の根幹に関わる基本的な問題が非常に多い．
我々は，この量子ウォークを光学系として解釈することより，波動力学の本質と基礎が得られると考えている．
例えば，ファインマンの著書「光と物質のふしぎな理論」の描像に従い，量子ウォークはフェルマーの原理を満たし，波面は光速で弾道的に進むと見ることができる．
さらに，量子ウォークの振る舞いは，ド・ブロイ・ボーム理論のパイロット波を想起する結果を得る．

Math-Fi seminar on 17 Apr.

2025.04.15 Tue up
  • Date: 17 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–19:00

  • Speaker 1: Dima Ivanenko (Taras Shevchenko National University of Kyiv)
  • Time: 16:50–17:50 
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES 3
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.

 
  • Speaker 2: Oleksii Kulik　 (Wroclaw University of Science and Technology)
  • Time: 18:00–19:00 
  • Title: A moments respecting explicit simulation scheme for L\’evy driven SDEs, I: Transformation of a heavy-tailed L\’evy noise by a dissipative drift
  • Abstract:
This is the first of two lectures devoted to the effect of tails/moments transformation by a dissipative drift for  solutions of SDEs driven by heavy-tailed noises.  In the first lecture we will discuss the history of the subject, illustrate how does this effect reveals itself in various settings, and provide a complete description of the effect in a general semi-martingale setting. 
 

Math-Fi seminar on 10 Apr. (Co-organized as a Quantum Walk Seminar)

2025.04.08 Tue up
 
  • Date: 10 Apr. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:50–17:50 
  • Speaker 1: Dima Ivanenko (Taras Shevchenko National University of Kyiv)
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES 2
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.
 
  • Speaker 2: Sohei Tateno (Nagoya University)
  • Time: 18:00–19:00 
  • Title: Iwasawa theory for discrete-time quantum walks in graphs
  • Abstract:
Transition matrices of discrete-time quantum walks in graphs are closely related to Ihara zeta functions of weighted graphs. For example, the celebrated Konno—Sato theorem has an application to calculate the eigenvalues of transition matrices. In this talk, by applying the methods of Iwasawa theory for graphs, we establish an asymptotic formula for the values of the characteristic polynomials of the transition matrices in a $\mathbb{Z}_p^d$-tower of graphs when an element of $\overline{\mathbb{Q}}_p$ is substituted to the polynomials. This is a joint work with Taiga Adachi and Kosuke Mizuno. 

Math-Fi seminar on 4 Apr.

2025.04.04 Fri up
  • Date: 4 Apr. (Fri.) 
     
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
     
  • Time: 16:30–18:00
     
  • Speaker:  Dima Ivanenko (Taras Shevchenko National University of Kyiv)
     
  • Title: ON APPROXIMATION OF SOME LÉVY PROCESSES
     
  • Abstract:
A Levy process X(t) has the structure X(t) = at + σW(t) + J(t) where W(t) is standard
Brownian motion (BM) and J(t) an independent pure jump process. This class of processes
has been used in numerous application areas, of which we in particular mention nance
and queueing. Calculations for a Levy process are, however, in general more dicult than
for BM, and an abundance of expressions that are explicit for BM are not so even in the
most popular parametric Levy models. Simulation of X(t) is therefore one of the main
computational tools.
A Levy process has countably many jumps on any interval [0, T] and nitely many jumps
of size bigger than some xed ε > 0. In order to simulate Z, we need to take nitely many
jumps of Z, which gives an adequate description of Z. Apart from some particular cases,
e.g. Brownian motion, Gamma process, α-stable process, simulation of the Levy process
with a given triplet is not an easy task.
Usually, the distribution function of a Levy process is unknown or has a rather compli-
cated form, which makes the simulation rather perplex. For the methods of generating
innitely divisible random variables (r.v.’s) and Levy processes (e.g. methods of Khinchin,
Fergusson-Klass, Bondesson, LePage, Rosinski) we refer to Rosinski (2001) and propose
our own method. We also would like to mention that the Damien-Laud-Smith algorithm
from Damien, Laud, and Smith (1995) gives a way to simulate an (approximation of)
an arbitrary onedimensional innitely divisible r.v., which allows us to simulate a Levy
process. On the other hand, it was observed by Bondesson (1982) and later by Asmussen
and Rosinski (2001), that under some conditions small jumps can be substituted by an
(arithmetic) Brownian motion.
The series of seminars includes a general theory of Levy processes, an overview of known
methods for modeling such processes, and a comparison of these methods with our own.

Math-Fi seminar on 30 Jan.

2025.01.29 Wed up
  • Math-Fi seminar on 30 Jan.
  • Date: 30 Jan. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time: 16:30–18:30
  • Speaker: Ritsusamuel Otsubo (Industrial Research Center of Shiga Prefecture)
  • Title: Study on Control for Hypothesis Testing of Dynamic Systems
  • Abstract: 
Currently, industrial product testing faces challenges such as a shortage of personnel and significant mental and physical burdens. As a result, automation has become an urgent necessity to address these issues. When testing components such as motors and hydraulic pistons, a method is employed where input is applied to the product, and its output is analyzed to determine whether it functions normally or abnormally. In such tests, it is crucial to develop a control system that can efficiently obtain the required information while minimizing the strain on both the test object and the equipment. Additionally, the system must maintain robustness against disturbances and noise to ensure reliable results.  In this seminar, we address hypothesis testing problems for parameters that characterize one-dimensional dynamic linear systems. The random disturbance of these systems is modeled as a stochastic variable defined on a space of continuous functions, characterized by its power spectral density. We also examine the behavior of linear systems under the influence of random disturbance. Additionally, we discuss an approximation of the random disturbance using the Ornstein-Uhlenbeck process. Based on these discussions, we consider the design of control systems to address these challenges. 
 

Math-Fi seminar on 23 Jan.

2025.01.23 Thu up
  • Date : 23 Jan. (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time : 16:30 – 18:45 
  • Speaker 1: Ryoji Takano (Osaka University) 16:30 –17:30
  • Title:On Some new integration by parts formula for finance and their Monte Carlo simulation
  • Abstract:
A rough volatility model is a stochastic volatility model for an asset price process with volatility being rough, meaning that the H\”{o}lder regularity of the volatility path is less than half. In this talk, we will focus on the asymptotic behavior of the implied volatility for the short maturity and show that the short-time large deviation principle for rough volatility models characterize the asymptotic behavior of the implied volatility.
 
 
  • Speaker 2:Yushi Hamaguchi (Kyoto University) 17:45 –18:45
  • Title: A generalized coupling approach for the weak approximation of stochastic functional differential equations
  • Abstract:
In this talk, we study functional type weak approximation of weak solutions of stochastic functional differential equations by means of the Euler–Maruyama scheme. Under mild assumptions on the coefficients, we provide a quantitative error estimate for the weak approximation in terms of the Lévy–Prokhorov metric of probability laws on the path space. The weak error estimate obtained in this paper is sharp in the topological and quantitative senses in some special cases. We apply our main result to ten concrete examples appearing in a wide range of science and obtain a weak error estimate for each model. The proof of the main result is based on the so-called generalized coupling of probability measures. This talk is based on a joint work with Dai Taguchi (Kansai University). The preprint is available at arXiv:2412.18523.

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