セミナー

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.

立命館大学数理工学セミナー（2022年8月4日（木））

2022.07.26 Tue up
<<立命館大学数理工学セミナー>>
日時：2022年8月4日（木） 16:30～18:00
講演者：
佐藤 寛之 （京都大学大学院情報学研究科）
題目：リーマン多様体上の最適化数理と非線形共役勾配法の一般的な枠組みについて
概要：
PDFファイルをご覧ください．

開催方法：
ウェストウィング6階談話会室での講演の模様をZoomミーティングで配信する予定です．
上記ファイル内に記載されたURLの申込フォームより8月3日（水）までにお申し込みください．
登録された方にセミナー当日の昼頃までにZoomミーティングの情報をお送りいたします．
対面参加を希望される方は、7月31日（日）までに多羅間へご連絡ください．
COVID-19の感染防止のため，対面参加者数が多い場合は適宜人数制限を行いますので，ご了承ください．
 
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.
 

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.

立命館大学幾何学セミナー（2022年7月15日（金））

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）
アブストラクト：
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.
 
開催方法： 
Zoomによる配信です．下記のURLより7月14日（木）までにご登録ください．
ご登録いただいた方に当日昼頃にZoomミーティングの情報をお送りします．
 
問い合わせ先：野澤 啓（立命館大学理工学部数理科学科）

立命館大学幾何学セミナー（2022年7月8日（金））

2022.07.02 Sat up
<<立命館大学幾何学セミナー>>
 
日時：2022年7月8日（金） 18:00～19:00

タイトル： Geometry of orbits of path group actions induced by Hermann actions

講演者： 森本 真弘 （大阪公立大学数学研究所）

アブストラクト：
こちらのPDFファイルをご覧ください．

開催方法：Zoom配信での開催です．

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

立命館大学数理工学セミナー（2022年6月30日（木））

2022.06.23 Thu up
<<立命館大学数理工学セミナー>>
日時：2022年6月30日（木） 17:30～19:00
講演者：
藤井 啓祐 （大阪大学基礎工学部，量子情報・量子生命研究センター）
題目：量子アルゴリズムの基礎と応用
概要：
PDFファイルをご覧ください．

開催方法：
ウェストウィング6階談話会室での講演の模様をZoomミーティングで配信する予定です．
上記ファイル内に記載されたURLの申込フォームより6月29日（水）までにお申し込みください．
登録された方にセミナー当日の昼頃までにZoomミーティングの情報をお送りいたします．
対面参加を希望される方は、6月26日（日）までに多羅間へご連絡ください．
COVID-19の感染防止のため，対面参加者数が多い場合は概ね30名程度以下となるよう適宜人数制限を行いますので，ご了承ください．
 
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 23 Jun.

2022.06.23 Thu up
  • Date: 23 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:00
  • Speaker: Kosuke Yamato (Kyoto University)
  • Title: A unifying approach to non-minimal quasi-stationary distributions for one-dimensional diffusions
  • Abstract:
In the present talk, we consider convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions. I will explain a method of reducing the convergence to the tail behavior of the lifetime via a property which we call the first hitting uniqueness. We apply the results to Kummer diffusions with negative drifts and give a class of initial distributions converging to each non-minimal quasi-stationary distribution.
 

Math-Fi seminar on 16 Jun.

2022.06.14 Tue up
  • Date: 16 Jun. (Thu.)
  • Place: W.W. 6th-floor, Colloquium Room and on the Web (Zoom)
  • Time: 16:30-18:30

  • Speaker 1: Tomoyuki Ichiba (University of California, Santa Barbara)
  • Title: Stochastic Differential Games on Random Directed Trees
  • Abstract:
We consider stochastic differential games on a random directed tree with mean-field interactions, where the network of countably many players is formulated randomly in the beginning and each player in the network attempts to minimize the expected cost over a finite time horizon. Here, the cost function is determined by the random directed tree. Under the setup of the linear quadratic stochastic game with directed chain graph, we solve explicitly for an open-loop Nash equilibrium for the system, and we find that the dynamics under the equilibrium is an infinite-dimensional Gaussian process associated with a Catalan Markov chain. We extend it to the random directed tree structures and discuss convergence results.
 
  • Speaker 2: Noriyoshi Sakuma (Nagoya City University)
  • Title: Selfsimilar free additive processes and freely selfdecomposable distributions
  • Abstract:
In the paper by Fan(2006), he introduced the marginal selfsimilarity of non-commutative stochastic processes and proved the marginal distributions of selfsimilar processes with freely independent increments are freely selfdecomposable. In this talk, we, first, give a short introduction of free probability. Then we introduce a new definition of selfsimilarity via linear combinations of non-commutative stochastic processes and prove the converse of Fan’s result, to complete the relationship between selfsimilar free additive processes and freely selfdecomposable distributions. Furthermore, we construct stochastic integrals with respect to free additive processes for constructing the background driving free L{\’e}vy processes of freely selfdecomposable distributions. A relation in terms of their free cumulant transforms is also given and several examples are also discussed. This talk is based on a joint work arXiv:2202.11848 with Makoto Maejima.
 

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