Seminars

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.

Math-Fi seminar on 16 Jan. (Co-organized as a Quantum Walk Seminar)

2025.01.10 Fri up
  • Date : 23 Jan. 2025 (Thu.) 
  • Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
  • Time : 16:00-19:30
  • Speaker: Keiichi Yokoyama（Japan Atomic Energy Agency）
  • Title:「量子ウォークを利用した同位体分離法の研究ーー社会実装へ向けた技術上の問題点と現状について」
  • Abstract:
放射性廃棄物の処理処分に同位体分離を組み込むことができれば、長寿命放射性核種の短寿命化や地層処分の大幅な負担軽減につながることがわかっている。しかし、現状よりもはるかに効率の良い同位体分離原理が必要であり、解決の目処はまったく立っていない。その中で、量子ウォークを用いることでこの問題を克服できる可能性が出てきた。理論上は、現状よりも数桁高い分離係数も可能であることが示された。これを受けて、社会実装のためにどのような技術的課題があるのか、検討が続いている。本セミナーにおいて、どのような課題があり、現在どのような状態にあるのか紹介する。

Math-Fi seminar on 9 Jan.

2025.01.09 Thu up
Date: 9 Jan (Thu) 18:00–19:30

Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)

Speaker: Taiho Wang (CUNY Baruch College) 

Title: Executions in competition under Erlang kernel

Abstract: 
We consider  the problem of multiple order executions in competition as differential games and investigate their associated equilibria in two regimes: Stackelberg and Nash games. Price impact during execution comprises of the components of permanent, transient with delay kernel of Erlang type, and temporary or slippage impacts. The Erlang type kernel provides the flexibility of specifying a maximal impact from the lagged past tradings as opposed to sheer decaying kernels such as exponential or power law. The resulting price impact model remains Markovian in an extended, but finite dimensional, state space. Dynamic programming principle is thus applicable and equilibria in the two differential games are obtained subject to solving systems of Riccati equations. Numerical experiments are conducted for illustration of the theoretical results. The talk is based on a joint work with Michele Aleandri and Marina Di Giacinto.

立命館大学作用素論セミナー

2025.01.09 Thu up
日時：2025年1月16日（木）16:30～17:30
 
場所：立命館大学BKCウエストウイング７階数学第４研究室
 
講演者：Trung Hoa Dinh (Troy University, Associated professor)
 
講演タイトル：Quantum divergences and bacycenters of positive definite matrices  
 
講演要旨：
In this talk, we review recent results on quantum divergences and explore related questions. Specifically, we examine the least squares problem with respect to various divergences, which introduces the concept of the barycenter of positive definite matrices. 

Math-Fi seminar on 19 Dec. (Ritsumeikan mini symposium on Quantum walk and related fields)

2024.12.19 Thu up
Date ：2024年12月19日（木）14:00 〜 18:10

Place: ：立命館大学BKCウエストウイング6階数理科学科談話会室＆ZOOM

Speaker 1 : SanThosh Kumar Pamula (Indian Institute of Science Education and Research (IISER) Mohali) 14:00-14:30

Title: Choi’s decomposition theorem for completely positive maps

Abstract:  In this talk we recall a few notions like inductive limit and projective limit of locally convex spaces and see that every locally C∗-algebra is a projective limit of family of associated　quotient C∗-algebras. We present a suitable approach to define the character space of commutative unital locally C∗-algebra via the notion of inductive limit of topological spaces. We prove that every commutative unital locally C∗-algebra A can be identified (through a Gelfand type representation) with the class of continuous functions defined on its character space of A . We call the spectrum of a locally bounded operator as a “local spectrum”, give a new notion of a locally C∗-algebra generated by a fixed locally bounded normal operator T and show that its character space is homeomorphic to the local spectrum of T. Finally, functional calculus and spectral mapping theorem will be discussed in this context.


Speaker 2 : Chaitanya J. Kulkarni (Indian Institute of Science Education and Research (IISER) Mohali) 14:30-15:00

Title: Stinespring dilation theorem

Abstract: In this talk, we will explore Stinespring’s dilation theorem for completely positive maps. This foundational result provides a characterization of completely positive maps from a C∗-algebra A into the bounded operators on a Hilbert space H denoted by B(H). The theorem demonstrates that such maps can be studied using a ∗-homomorphism from A into B(K) for some other Hilbert space K. We will outline a proof of this theorem and discuss remarks and implications for specific classes of completely positive maps.


Speaker 3 : 石和田瞳 (立命館大学) 15:00-15:30

Title: Excursions of quantum walks

Abstract: We will introduce the notions of hitting time, sojourn time, and excursion of quantum walks on the real line, aiming to obtain results analogue to the classical cases.


Speaker 4 : 穂坂大将（横浜国立大学）15:40-16:10

Title: 空間的な摂動を与えた量子ウォークの挙動について

Abstract:本講演では、有限グラフに対して空間的な摂動を与えたようなグラフ上で量子ウォークを時間発展させた際の挙動について考察をする。特に、今回はジョンソングラフと呼ばれるグラフに対し、スターグラフを摂動として与えたグラフ上において、ほとんど全ての量子ウォークが周期的にスターグラフへ集められるような挙動を取ることが固有値解析の結果判明したので紹介する。このような現象のことを本講演では拍動現象と呼ぶ。拍動現象は、量子探索アルゴリズムの一種の拡張とも考えられるため、それらについてもシミュレーションなどを用いて紹介する。


Speaker 5 : 関藤寛人（横浜国立大学）16:10-16:40

Title: TBA

Abstract: TBA


Speaker 6 : 山上智輝 （東京大学） 16:50-17:30

Title: 量子ウォーク探索によるグラフ上の最適腕識別

Abstract: ある環境に与えられた複数のスロットマシン（腕）の中から，より素早く最も報酬期待値の高い腕を特定する最適腕識別という問題を，量子振幅増幅を用いて解くアルゴリズムが先行研究で提案されている。本講演では，量子ウォークを用いてこのアルゴリズムを拡張することで，環境が空間構造を持つ，即ち腕がグラフ上に配置されている場合における最適腕識別の手法を提案する。


Speaker 7 : 関元樹（北海道大学） 17:30-18:10

Title: 2次元2状態量子ウォークの弱収束定理

Abstract:  量子ウォークはランダムウォークの量子版と呼ばれる数理モデルである。量子ウォークの最も大きな話題の1つとして弱収束定理がある。これまで，1次元の量子ウォークの弱収束定理は一様な場合と，非一様な場合の双方において研究されており，その多くの極限分布には今野関数と呼ばれる初期状態に依存しない特有な関数があらわれる。
一方，2次元の量子ウォークについては一般化されたGroverウォークの弱収束定理が先行研究として知られている。本研究では先行研究を特殊な場合として含む，一様な2次元2状態の量子ウォークについて極限分布を導出した。特にここで得られた確率密度関数についてある種の極限を取ると1次元量子ウォークにおける今野関数が導かれる。
本講演では，本研究のエッセンスのエッセンスと解析内容の概要を述べる。

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