11 citations · 18 across the 6 of their papers we have counts for
6 papers
Reflecting brownian motion and the gauss-bonnet-chern theorem
Weitao Du, Elton P. Hsu
We use reflecting Brownian motion (RBM) to prove the well known Gauss-Bonnet-Chern theorem for a compact Riemannian manifold with boundary. The boundary integrand is obtained by ca…
Geometric Deviation From Lévy's Occupation Time Arcsine Law
Elton P. Hsu, Cheng Ouyang
We prove a geometric extension of Lévy's occupation time arcsine law near a hypersurface on a Riemannian manifold. The deviation from the classic arcsine law is of the order of the…
Bismut's gradient formula for vector bundles
Elton P. Hsu, Zhenan Wang
We prove a general Bismut's formula for the gradient of a class of smooth Wiener functionals over vector bundles of a compact Riemannian manifold. This general formula can be used…
Computation of Local Time of Reflecting Brownian Motion and Probabilistic Representation of the Neumann Problem
Yijing Zhou, Wei Cai, Elton Hsu
In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R3 and its use in the probabilistic representation of the s…
Stochastic De Giorgi Iteration and Regularity of Stochastic Partial Differential Equation
Elton P. Hsu, Yu Wang, Zhenan Wang
Under general conditions we show that the solution of a stochastic parabolic partial differential equation of the form \[ \partial_t u = \mathrm{div} (A \nabla u) + f(t,x, u) + g_i…
Volume growth and escape rate of Brownian motion on a complete Riemannian manifold
Elton P. Hsu, Guangnan Qin
We give an effective upper escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth of the manifold. An important step in the work i…