Speed of Convergence to Equilibrium of Random Dynamical Systems - With Applications


Rabi Bhattacharya (Department of Mathematics, University of Arizona)
  1. MMDSについて
  2. MMDSの教員・組織
  3. MMDSで学びたい方へ
  4. カリキュラム
  5. MMDSの活動

  6. 学内向け情報

大阪大学 金融・保険セミナーシリーズ 第40回(CSFI-CRESTジョイントセミナー)
Speed of Convergence to Equilibrium of Random Dynamical Systems - With Applications

Rabi Bhattacharya (Department of Mathematics, University of Arizona)

Markov processes in discrete time on a standard state space S are of the form Xn = αn…α1X0, where αn (n=1,2,…) are i.i.d. random maps on S, independent of the initial state X0. For processes of interest here, S is a partially ordered metric space and αn are monotone maps on S into S. We find conditions for the existence of a unique equilibrium π and compute the speed of convergence of Xn to π in an appropriate distance. Applications are given to some growth and ruin problems in economics and insurance, and to the 2D Ising model on finite lattices. In continuous time we consider processes Xt (t≥0) on S= R^k (k≥1) governed by Ito’s stochastic differential equation dXt = b(Xt)dt + σ(Xt)dBt, with an initial X0 independent of the k-dimensional Brownian motion Bt (t≥0). Of particular interest are slow (i.e., polynomial) convergence rates to equilibrium signifying long range dependence.

講 師:
Rabi Bhattacharya (Department of Mathematics, University of Arizona)
テーマ:
Speed of Convergence to Equilibrium of Random Dynamical Systems - With Applications
日 時:
2012年06月29日(金)13:00-14:30
場 所:
大阪大学大学院基礎工学研究科 (豊中キャンパス)J棟7階J706号室
参加費:
無料
アクセス:
会場までのアクセスは下記URLをご参照ください。
http://www.es.osaka-u.ac.jp/access/
お問い合せ:
本ウェブサイトの「お問い合せ」のページをご参照ください。