4 papers
Estimates of the numerical density for stochastic differential equations with multiplicative noise
Lei Li, Mengchao Wang, Yuliang Wang
We investigate the estimates of the density for the traditional Euler-Maruyama discretization of stochastic differential equations (SDEs) with multiplicative noise. Our estimates f…
A modified tamed scheme for stochastic differential equations with superlinear drifts
Zichang Ju, Lei Li, Yuliang Wang
Explicit discretizations of stochastic differential equations often encounter instability when the coefficients are not globally Lipschitz. The truncated schemes and tamed schemes…
A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics
Lei Li, Yuliang Wang
We establish a sharp uniform-in-time error estimate for the Stochastic Gradient Langevin Dynamics (SGLD), which is a widely-used sampling algorithm. Under mild assumptions, we obta…
Propagation of chaos in path spaces via information theory
Lei Li, Yuelin Wang, Yuliang Wang
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stocha…