We propose a new numerical scheme for a class of one-dimensional reflected stochastic differential equations (SDEs) by virtue of their explicit solutions, which enables us to carry out the simulation of this class of reflected SDEs by simulating some related SDEs without reflections. The new...

In this article we suggest a new method for solutions of stochastic integrals where the dynamics of the variables in integrand are given by some stochastic differential equation. We also propose numerical simulation of stochastic differential equations which is based on iterated integrals method...

We show a new higher order weak approximation with Malliavin weights for multidimensional stochastic differential equations by extending the method in Takahashi and Yamada (2016). The estimate of global error of the discretization is based on a sharp small time expansion using a Malliavin...

This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether...

This work contributes a systematic survey and complementary insights of reflecting Brownian motion and its properties. Extension of the Skorohod problem's solution to more general cases is investigated, based on which a discussion is further conducted on the existence of solutions for a few...

This paper proposes a new third-order discretization algorithm for multidimensional Itô stochastic differential equations driven by Brownian motions. The scheme is constructed by the Euler-Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply...