Hellinger and total variation distance in approximating L{é}vy driven SDEs

Milstein's type schemes for fractional SDEs

Weighted power variations of fractional Brownian motion B are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by B. The limit of the error between the exact solution and the considered scheme is computed explicitly.

Numerical Computations for Backward Doubly SDEs and SPDEs

In this paper we present two numerical schemes of approximating solutions of backward doubly stochastic differential equations (BDSDEs for short). We give a method to discretize a BDSDE. And we also give the proof of the convergence of these two kinds of solutions for BDSDEs respectively. We give a sample of computation of BDSDEs.

On Markovian semigroups of Lévy driven SDEs, symbols and pseudo--differential operators

We analyse analytic properties of nonlocal transition semigroups associated with a class of stochastic differential equations (SDEs) in $\mathbb{R}^d$ driven by pure jump--type Lévy processes. First, we will show under which conditions the semigroup will be analytic on the Besov space $B_{p,q}^ m(\mathbb{R}^d)$ with $1\le p, q<\infty$ and $m\in\mathbb{R}$. Secondly, we present some applications by proving the strong Feller property and give weak error estimates for approximating schemes of the SDEs over the Besov space $B_{\infty,\infty}^ m(\mathbb{R}^d)$.

Approximation of heavy-tailed distributions via stable-driven SDEs

Constructions of numerous approximate sampling algorithms are based on the well-known fact that certain Gibbs measures are stationary distributions of ergodic stochastic differential equations (SDEs) driven by the Brownian motion. However, for some heavy-tailed distributions it can be shown that the associated SDE is not exponentially ergodic and that related sampling algorithms may perform poorly. A natural idea that has recently been explored in the machine learning literature in this context is to make use of stochastic processes with heavy tails instead of the Brownian motion. In this pape…

由G-Brownian运动驱动的双重反射倒向随机微分方程与带有双重障碍的完全非线性偏微分方程

Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles

本文提出通过单调递减的惩罚反射G-BSDE逼近解的新方法，在已知最弱条件下证明了双重反射G-BSDE解的适定性，并首次揭示其与带双重障碍的完全非线性偏微分方程的关系。

SDEs驱动的系统well-posedness研究

Well-posedness of a system of SDEs driven by jump random measures

本文研究了具有非Lipschitz系数的SDE系统well-posedness，通过路径唯一性证明和比较定理，构建了非负可积解，并讨论了金融建模中的应用。