Math-Fi seminar on 6 Sep.

2022.09.05 Mon up
  • Date: 6 Sep. (Tue.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Dan Crisan (Imperial College London)
  • Title: Classical and modern results in the theory and applications of stochastic filtering
  • Abstract:
Onwards from the mid-twentieth century, the stochastic filtering problem has caught the attention of thousands of mathematicians, engineers, statisticians, and computer scientists. Its applications span the whole spectrum of human endeavour, including satellite tracking, credit risk estimation, human genome analysis, and speech recognition. Stochastic filtering has engendered a surprising number of mathematical techniques for its treatment and has played an important role in the development of new research areas, including stochastic partial differential equations, stochastic geometry, rough paths theory, and Malliavin calculus. It also spearheaded research in areas of classical mathematics, such as Lie algebras, control theory, and information theory. The aim of this talk is to give a historical account of the subject concentrating on the continuous-time framework. I will also present a recent application of filtering to the estimation of partially observed high dimensional fluid dynamics models. In particular, I will introduce a so-called particle filter that incorporates a nudging mechanism. The nudging procedure is used in the prediction step. In the absence of nudging, the particles have trajectories that are independent solutions of the model equations. The nudging presented here consists in adding a drift to the trajectories of the particles with the aim of maximising the likelihood of their positions given the observation data. This introduces a bias in the system that is corrected during the resampling step.  The methodology is tested on a two-layer quasi-geostrophic model for a beta-plane channel flow with O(10^6) degrees of freedom out of  which only a minute fraction are noisily observed. 
The talk is based on the papers:
[1] D Crisan, The stochastic filtering problem: a brief historical account, Journal of Applied Probability 51 (A), 13-22
[2] C Cotter, D Crisan, D Holm, W Pan, I Shevchenko, Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise,  Journal of Statistical Physics, 1-36, 2020.
[3] D Crisan, I Shevchenko, Particle filters with nudging, work in progress.


2022.08.27 Sat up
日時:2022年9月1日(木) 16:30~17:30
Wolfram Bauer (Leibniz Universität Hannover)
題目:Subriemannian geometry and analysis of associated operators


問い合わせ先:立命館大学理工学部数理科学科 高橋 典寿

2022年12月16日(金) — 18日(日) ワークショップ

2022.08.22 Mon up
Workshop “2022 Japan-China International Conference on matrix theory with applications”

Date : December 16 (Friday)  – December 18 (Sunday), 2022

Place: Colloquium Room, West Wing Building 6F 
 Biwako Kusatsu Campus, Ritsumeikan University
 Kusatsu City, Shiga, Japan
 No. 9 Building in <http://www.ritsumei.ac.jp/campusmap/bkc/> 

Holding form : Hybrid format
Chinese side will give a lecture only online

Registration           Schedule          Abstracts

Speakers :
—Plenary talks—
  • Etsuo Segawa (Yokohama National University)
  • Lee Jaeha (University of Tokyo)
—General Talks—
  • Michiya Mori(RIKEN)  (confirmed) 
  • Shiho Oi (Niigata University(confirmed)
  • Tomohiro Hayase (Cluster inc.)  (confirmed)
  • Yoichi Udagawa (Ritsumeikan University) (confirmed)
  • Toshikazu Abe (Ibaraki University(confirmed)
  • Ryo Takakura (Kyoto University (confirmed)
  • Zhi-Gang Jia (Jiangsu Normal University)
  • Tie-Xiang Li (Southeast University)
  • Kan He (Taiyuan University of Technology)
  • Xiaomin Pan (Shanghai University)
  • Jianzhou Liu (Xiangtan University)
  • Bing Zheng (Xiangtan University)
  • Guang-Jing Song (Weifang University)
  • Jinchuan Hou (Taiyuan University of Technology)

Local organizing Committee :
Hiroyuki Osaka (Ritsumeikan University)
Yoichi Udagawa (Ritsumeikan University)
Masaru Nagisa (Ritsumeikan University)
Scientific Organizing Committee :
Zhuo-Heng He (Shanghai University)
Takaaki Yamazaki (Toyo 
Yuki Seo (Osaka Education 
Hiromichi Ohno (Shinshu 
Gen Kimura (Shibaura Institute of Technology)

数理科学科談話会 (2022/7/29)

2022.07.26 Tue up
学外からご参加いただける場合は原則,zoom(オンライン)上での参加をお願いいたします.ご参加の場合は中川(nkgw-t@fc.ritsumei.ac.jp )までご連絡ください.
タイトル: 量子ウォークからゼータ対応へ
ここ一年程にわたる我々の一連のゼータ対応シリーズは,無限グラフに関する先行結果を,離散時間のグローバー型量子ウォークに対する今野・佐藤の定理 (2012) をトーラスに適用することにより同じ表式が導出可能であることに気づくことから誕生した.それ以降,「新しいタイプのゼータ関数」を適宜導入することにより,グローバー型だけでなく,全ての量子ウォークでも適用可能であり,また,ランダムウォーク,相関付ランダムウォーク,開量子ランダムウォーク,さらに,量子ウォークの正台のような通常の意味でウォークといえないモデルまで扱えることが明らかになった.一方,上述の一粒子系だけでなく,多粒子系(確率セルオートマトンや量子セルオートマトンなど),また対応する連続時間モデルまで拡張可能であることも分かった.ごく最近では,数論,トロピカル幾何,可積分系とも密接な関連があるマーラー測度との関係も見いだされた.本講演では,量子ウォークを概説した後に,ゼータ対応シリーズの中から,量子ウォークに関連する内容を主に紹介したい.


2022.07.26 Tue up
日時:2022年8月4日(木) 16:30~18:00
佐藤 寛之 (京都大学大学院情報学研究科)

問い合わせ先:立命館大学理工学部数理科学科 多羅間 大輔

Math-Fi seminar on 26 Jul.

2022.07.25 Mon up
  • Date: 26 Jul. (Tue.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Kei Noba (The Institute of Statistical Mathematics)
  • Title: Optimality of classical or periodic barrier strategies for Lévy processes
  • Abstract:
We revisit the stochastic control problem in two cases with Lévy processes that minimize running and controlling costs. Existing studies have shown the optimality of classical or periodic barrier strategies when driven by Brownian motion or Lévy processes with one-sided jumps. Under the assumption that we can be controlled at any time or only at Poissonian dividend-decision times, we show the optimality of classical or periodic barrier strategies for a general class of Lévy processes.

数理科学科談話会 (2022/7/21)

2022.07.20 Wed up
学外からご参加いただける場合は原則,zoom(オンライン)上での参加をお願いいたします.ご参加の場合は平良(ktaira@fc.ritsumei.ac.jp )までご連絡ください.
タイトル: Malliavin-Sokorohod calculus for canonical Lévy processes with applications
アブストラクト: In this talk, we deal Malliavin-Sokorohod (MS, in short) calculus for canonical Lévy processes with applications, especially mathematical finance. MS calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of ‘’derivatives” of random variables, such as functionals for Lévy processes, stochastic integrals and stochastic differential equations.  MS calculus is also called the stochastic calculus of variations. 
 The first half of the presentation, we introduce MS calculus for canonical Lévy processes. Especially, we use chaos expansion, derivative operator and increment quotient difference operator for Lévy functionals. Calculations tools about MS calculus are also introduced. By using the results, we next derive a new modified $\Phi$-Sobolev type inequalities for canonical Lévy processes and we also derive concentration inequalities. Moreover, asymptotic estimates for their inequality will be given. 
 The second half of the presentation will address issues to mathematical finance. In particular, we consider locally risk minimizing hedging strategies, a typical hedging technique in incomplete markets. The presentation will introduce a method using Malliavin analysis, which provides a concrete expression formula and can be applied to numerical analysis and other practical problems. The use of Malliavin analysis provides concrete expression formulas, which can be applied to numerical analysis and other practical applications.
 In the remaining time, we will discuss future prospects.
タイトル:グラフ上のラプラシアンに対する Gel’fand の問題

Math-Fi seminar on 14 Jul.

2022.07.13 Wed up
  • Date: 14 Jul. (Thu.)
  • Place: On the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Takuji Arai (Keio University)
  • Title: Constrained optimal stopping under a regime-switching model
  • Abstract:
We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times and only during a specific regime. The main objectives are to show that an optimal stopping time exists as a threshold type under some boundary conditions and to derive expressions of the value functions and the optimal threshold. To this end, we solve the corresponding variational inequality and show that its solution coincides with the value functions. Some numerical results are also introduced. Furthermore, we investigate some asymptotic behaviors. This talk is based on joint work with Masahiko Takenaka.

Math-Fi seminar on 7 Jul.

2022.07.06 Wed up
  • Date: 7 Jul. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Pierre Bras (Sorbonne Université)
  • Title: Asymptotics for the total variation distance between an SDE and its Euler-Maruyama scheme in small time
  • Abstract:
We give bounds for the total variation distance between the law of an SDE and the law of its one-step Euler-Maruyama scheme as $t \to 0$. The case of the total variation is more complex to deal with than the classic case of Wasserstein ($L^p$) distances. We show that this distance is of order $t^{1/3}$, and more generally of order $t^{r/(2r+1)}$ for any $r \in \mathbb{N}$. Improving the bounds from $1/3$ to $r/(2r+1)$ relies on a weighted multi-level Richardson-Romberg extrapolation which consists in linear combination annealing the terms of a Taylor expansion, up to some order. This method was introduced for bias reduction in practical problems, but is used here for theoretical purposes.


2022.07.05 Tue up
日時:2022年7月15日(金) 16:30–18:00
タイトル: Generalized Thouless formula
講演者: 高橋 悠樹氏 (埼玉大学)
It is well-known that the density of states measure of the one dimensional ergodic Schrodinger operator agrees with the Laplacian of the associated Lyapunov exponent (in the sense of distribution). We extend the above result to monotonic cocycles.
問い合わせ先:野澤 啓(立命館大学理工学部数理科学科)