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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations principle for weighted means of a recursive numerical method for ergodic SDEs
遍历 SDE递归 数值方法 加权均值 大偏差原理
2023/4/24
For ergodic SDEs, their ergodic limits are usually approximated by the suitable means of numerical methods. To reveal the numerical asymptotic behavior, we study the large deviations principle (LDP) f...
In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomizati...
Local Holder continuity property of the Densities of Solutions of SDEs with Singular Coefficients
Malliavin Calculus non-smooth drift density function Probability
2012/6/21
We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and H\"{o}lder continuous drift has a H\"{o}lder continuous density f...
Derivative Formula, Integration by Parts Formula and Applications for SDEs Driven by Fractional Brownian Motion
Derivative formula integration by parts formula Harnack inequality stochastic differential equation fractional Brownian motion
2012/6/21
In the paper, the Bismut derivative formula is established for multidimensional SDEs driven by additive fractional noise ($1/2
Multilevel Monte Carlo method for jump-diffusion SDEs
Multilevel Monte Carlo method jump-diffusion SDEs expected payoff jump rates
2011/7/4
We investigate the extension of the multilevel Monte Carlo path
simulation method to jump-diffusion SDEs. We consider models with
finite rate activity , using a jump-adapted discretisation in which ...
Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
Harnack inequality functional solution delay SDE strong Feller property
2011/2/28
By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong...
High order weak approximation schemes for Lévy-driven SDEs
Levy-driven stochastic di erential equation Euler scheme
2011/2/28
We propose new jump-adapted weak approximation schemes for stochas-tic di erential equations driven by pure-jump Levy processes.
Second order discretization of Backward SDEs
Backward SDEs Second order Numerical analysis
2011/2/28
In [5] the authors suggested a new algorithm for the numerical approximation of a BSDE by merging the cubature method with the first order discretization developed by Bouchard and Touzi [3] and Zhang ...
In this article, a class of second order differential equations on [0,1], driven by a general H\"older continuous function and with multiplicative noise, is considered. We first show how to solve thi...
Obstacle problem for SPDE with nonlinear Neumann boundary condition via reflected generalized backward doubly SDEs
SPDE nonlinear Neumann boundary condition
2010/11/19
This paper is intended to give a representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use i...
Reflected Generalized Backward Doubly SDEs driven by Lévy processes and Applications
Doubly SDEs Lévy processes Applications
2010/11/19
In this paper, we study reflected generalized backward doubly stochastic differential equations driven by Teugels martingales associated with L\'evy process (RGBDSDELs, in short) with one continuous ...
On the rate of convergence of weak Euler approximation for non-degenerate SDEs
L´ evy processes stochastic differential equations
2010/12/10
The paper estimates the rate of convergence of the weak Euler approximation for solutions to SDEs driven by point and martingale measures, with H¨older continuous coefficients. The equation considered...
An Exact Connection between two Solvable SDEs and a Non Linear Utility Stochastic PDEs
forward utility performance criteria horizon-unbiased utility
2010/10/20
The paper proposes a new approach to consistent stochastic utilities, also called forward dynamic utility, recently introduced by M. Musiela and T. Zariphopoulou. These utilities satisfy a property of...
Well-posedness and large deviation for degenerate SDEs with Sobolev coefficients
Well-posedness large deviation SDEs Sobolev coefficients
2010/3/11
In this article we prove the existence and uniqueness for degenerate stochastic differential
equations with Sobolev (possibly singular) drift and diffusion coefficients in a generalized
sense. In pa...
Nonlinear SDEs driven by Lévy processes and related PDEs
Particlesystems Propagationofchaos Nonlinear stochastic differential equations driven by Levy processes
2009/6/12
In this paper we study general nonlinear stochastic differential equations,where the usual Brownian motion is replaced by a Levy process.Moreover,we do not suppose that the coefficient multiplying the...