- 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.