Monte Carlo estimation of the solution of fractional partial differential equations

带分数核的随机Volterra方程的多层Monte Carlo Euler估计量的中心极限定理

Central limit theorem of Multilevel Monte Carlo Euler estimators for Stochastic Volterra equations with fractional kernels

本文证明了带分数核的随机Volterra方程在Euler离散化下多层Monte Carlo估计量满足Lindeberg-Feller型中心极限定理。

On the optimality of the Monte-Carlo estimator

We prove that on an atomless probability space, the worst-case mean squared error of the Monte-Carlo estimator is minimal if the random points are chosen independently.

Nesting Monte Carlo for high-dimensional Non Linear PDEs

A new method based on nesting Monte Carlo is developed to solve high-dimensional semi-linear PDEs. Convergence of the method is proved and its convergence rate studied. Results in high dimension for different kind of non-linearities show its efficiency.

Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations

The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical approach based on Monte Carlo integration to simulate solutions of fractional ordinary and partial differential equations. Thirdly, we show that this approach allows us to find the fundamental solutions for fractional partial differential equations (PDEs), in which the fractional derivative in time is in the Caputo sense and the fractional in space one is in the…

多级拟蒙特卡洛积分的快速正交变换

Fast orthogonal transforms for multi-level quasi-Monte Carlo integration

结合通用快速正交变换方法与多级蒙特卡洛方法，提升拟蒙特卡洛积分效率。

Monte-Carlo simulations for wall-bounded fluid flows via random vortex method

In this paper a Monte-Carlo method for simulating the motion of fluid flow moving along a solid wall is proposed. The random vortex method in the present paper is established by using the reflection technology and perturbation technique. The Monte-Carlo method based on this random vortex dynamic may be implemented, and several Monte-Carlo simulations are then carried out for the flows near the solid wall.