ニュース＆イベント

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
7月21日（木）に談話会を開催します．
 
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．
 
日程：7月21日（木）16:30-19:00
場所：立命館大学BKCキャンパスウエストウイング談話会室（対面とzoomのハイブリッド開催）
 
16:30-17:30：鈴木良一（立命館大学）
 
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.
 
 
18:00-19:00：磯崎洋（立命館大学）
 
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.

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.
 

立命館大学幾何学セミナー（2022年6月24日（金））

2022.06.13 Mon up
<<立命館大学幾何学セミナー>>

日時： 2022年6月24日（金） 18:00～19:00

タイトル： Jacobi構造とRiemann計量の整合性

講演者： 中村 友哉 （工学院大学）

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

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