## 2020年度

### Math-Fi seminar on 7 May

2020.05.07 Thu up
• Date: 7 May (Thu.)
• Place: On the Web
• Time: 16:30-18:00
• Speaker: Takuya Nakagawa (Ritsumeikan University)
• Title: On a Monte Carlo scheme for a stochasticquantity of SPDEs with discontinuous initial conditions
• Abstract:
The aim of this seminar is to study the simulation of an expectation of a stochastic quantity $\e[f(u(t,x))]$ for a solution of stochastic partial differential equation driven by multiplicative noise with a non-smooth coefficients and a boundary condition: $Lu(t,x)=h(t,x) \dot{W}(t,x)$.
We first define a Monte Carlo scheme $P_{t}^{(N,M,L)}f(x)$ for $P_{t}f(x):=\e[f(u(t,x))]$, where $f$ is a bounded measurable function $f$ and $u(t,x)$ is a solution of stochastic partial differential equation given by Duhamel’s formula, and then we prove the convergence of the Monte Carlo scheme $P_{t}^{(N,M,L)}f(x)$ to $P_{t}f(x)$ and  the rate of weak error.
In addition, we introduce results of numerical experiments about the convergence error and the Central limit theorem for the scheme.

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