ニュース＆イベント

Math-Fi seminar on 29 Jul.

2021.07.28 Wed up
  • Date: 29 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Takuya Nakagawa (Ritsumeikan University)
  • Title: Projection scheme for polynomial diffusions on the unit ball
  • Abstract:
In this talk, we consider numerical schemes for polynomial diffusions on the d-dimensional unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form (1-|x|^{2})^{1/2}. We introduce a projection scheme on the unit ball based on a backward Euler–Maruyama scheme with the projection and provide the L^{2}-rate of convergence. The main idea to consider the numerical scheme is a transformation argument introduced by Swart, J. M. (2012) for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient. This study is a joint work with Dai Taguchi and Tomooki Yuasa.

Math-Fi seminar on 22 Jul.

2021.07.21 Wed up
  • Date: 22 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Lorenzo Marino (Université d’Evry Val d’Essonne, University of Pavia)
  • Title: Weak Regularization by Degenerate Lévy noise and Applications
  • Abstract:
In this talk, we briefly present the arguments of the PhD thesis: “Weak Regularization by Degenerate Lévy noise and Applications”. After a general introduction on the regularization by noises phenomena and the motivations behind this work, we start by showing the Schauder estimates, a useful analytical tool for the wellposedness of SDEs, for two different classes of integro-differential equations whose coefficients lie in suitable anisotropic Hölder spaces with multi-indices of regularity. The first one focuses on non-linear dynamics controlled by an α-stable operator acting only on the first component. To deal with the non-linear perturbation, we also need some subtle controls on Besov norms. As an extension of the first one, we also present the Schauder estimates associated with a degenerate Ornstein-Uhlenbeck operator driven by a larger class of α-stabletype operators, like the relativistic or Lamperti stable ones. The proof of this result relies instead on a precise analysis of the behaviour of the associated Markov semigroup between anisotropic Hölder spaces and some interpolation techniques. Exploiting a backward parametrix approach, we finally prove the weak wellposedness of the associated degenerate chain of SDEs. As a by-product of our method, Krylov-type estimates on the canonical solution process are also presented. Time permitting, we conclude by showing through suitable counter-examples that there exists an (almost) sharp threshold for the regularity exponents that ensure the weak well-posedness for the SDE.
 

Math-Fi seminar on 8 Jul.

2021.07.07 Wed up
  • Date: 8 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Shota Nakamura (Waseda University)
  • Title: 長期記憶性を持つサープラスの破産確率の推定
  • Abstract:
クーレムが長期記憶性を持つような保険会社のサープラスの推定問題を考える.
この様なモデルは近似的にハースト指数H>1/2を持つ非整数ブラウン運動で表現することができる. 本セミナーでは,非整数ブラウン運動で表現されるサープラスのモデルが持つ未知パラメータの漸近正規性を持つ推定量が与えられた際の,破産確率の推定量の漸近分布のMalliavin解析を用いた導出法について概説を行う.

立命館大学数理工学セミナー（2021年7月15日（木））

2021.07.06 Tue up
<<立命館大学幾何学セミナー>>

日時：2021年7月15日（木） 16:30～18:00

タイトル：信号の情報量とフィードバック制御系の性能

講演者：岡野 訓尚 （立命館大学理工学部）

アブストラクト：
通信機能を備えたセンサやアクチュエータが普及し，制御システムにおいても有線/無線を問わず通信ネットワークの利用が広がっている．
本セミナーでは，低速な回線でフィードバック制御を行う場面を想定し，どの程度まで情報量を落とすと制御が破綻する（安定化できなくなる）か，どのような情報を優先して通信すべきか，といった問題について取り上げ，基礎的な結果から最近の研究も含めて紹介する．

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

Math-Fi seminar on 1 Jul.

2021.06.30 Wed up
  • Date: 1 Jul. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Roger Pettersson (Linnaeus University)
  • Title: Epidemic modeling on microscopic, macroscopic and mesoscopic scale: the Kurtz’ approach
 

Math-Fi seminar on 24 Jun.

2021.06.23 Wed up
  • Date: 24 Jun. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Maria Elvira Mancino (University of Florence)
  • Title: Volatility and higher order covariances estimation for identifying financial instability conditions and computing hedging Greeks
  • Abstract:
I would present the most recent papers with Simona, both of them use the same mathematical instruments for different applications. Further, it is based on some ideas presented in the paper with Malliavin  “”Harmonic analysis methods for nonparametric estimation of volatility: theory and applications””. In  Proceedings of the International Symposium “Stochastic Processes and Applications to Mathematical Finance” 2005 at Ritsumeikan University, World Scientific (2006).  Eds. J.Akahori, S.Ogawa, S.Watanabe.

Math-Fi seminar on 17 Jun.

2021.06.17 Thu up
  • Date: 17 Jun. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Olivier Menoukeu Pamen (African Institute of Mathematical Sciences and University of Liverpool)
  • Title:Takagi type functions and dynamical systems: the smoothness of the SBR measure and the existence of local time
 

Math-Fi seminar on 10 Jun.

2021.06.09 Wed up
  • Date: 10 Jun. (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Pierre Bras (Sorbonne University, LPSM)
  • Title: Convergence rates of Gibbs measures with degenerate minimum
  • Abstract:
We study convergence rates of Gibbs measures, with density $\pi_t(dx) \propto e^{-f(x)/t} dx$, as $t \to 0$ and where $f: \mathbb{R}^d \to \mathbb{R}$ admits a unique global minimum at $x^\star$. If the Hessian matrix $\nabla^2 f(x^\star)$ is positive definite then a Taylor expansion up to order 2 shows that $\pi_t$ converges to the Dirac measure $\delta_{x^\star}$ at speed $\sqrt{t}$.
We focus on the case where the Hessian of $f$ is not definite at $x^\star$. We assume instead that the minimum is strictly polynomial and we give a higher order nested expansion of $f$ at $x^\star$. We give an algorithm yielding such decomposition, in connection with Hilbert’s $17^{th}$ problem. We then give the rate of convergence of $\pi_t$ using this expansion.
Our work can be applied to stochastic optimization, where the Gibbs measure $\pi_t$ with small $t$ is used as an approximation of the minimizer of $f$.
 

立命館大学数理工学セミナー（2021年5月31日（月））

2021.05.27 Thu up
<<立命館大学幾何学セミナー>>

日時：2021年5月31日（月） 16:30～18:00

タイトル：
プラズマ乱流が励起する非線形構造と核融合閉じ込めへの応用

講演者：
小菅 佑輔 （九州大学）

アブストラクト：
本セミナーでは、世界各国で精力的に進められている核融合研究について紹介し、その閉じ込め性能を理解する上で必要となるプラズマ乱流研究について解説する。特に、プラズマ乱流が駆動する非線形構造に焦点をあて、我々のグループで進めている励起過程の理解や制御を目指した研究について紹介する。これらの研究を支える代表的なモデルについて触れ、非線形Schroedinger方程式に基づく非線形構造励起の研究や、ハミルトン構造を有する方程式系（Vlasov方程式や２次元乱流系を記述するCharney-Hasegawa-Mima方程式や運動論的乱流を記述するVlasov 方程式）に基づく緩和研究などを紹介する。

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

Math-Fi seminar on 20 May

2021.05.19 Wed up
  • Date: 20 May (Thu.)
  • Place: On the Web
  • Time: 16:30 – 18:00
  • Speaker: Libo Li (University of New South Wales)
  • Title: Random times and RBSDEs
  • Abstract:
In this talk, we will discuss three related topics. The first is the additive and multiplicative representation of the survival process of a finite honest time. We show that the survival process can be expressed as drawdown and relative drawdown of some optional supermartingale with continuous running supremum, and we recover the Madan-Roynette-Yor option pricing formula involving  the last passage times of zero for optional semimartingales of class-sigma. The second is the construction of random time, where we extend using, multiplicative systems, the Madan-Roynette-Yor to all positive optional supermartingale and apply our results to construct random time with a given survival process. Finally motivated by the arbitrage-free pricing of European and American style contracts with the counterparty credit risk, we investigate the well-posedness of BSDE and RBSDE in the progressive enlargement of a reference filtration with a random time through the method of reduction.

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