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math.PR2019
Explicit form of the effective evolution equation for the randomly forced Schrödinger equation with quadratic nonlinearity
Huilin Zhang, Elena Tobisch
An effective equation describes a weakly nonlinear wave field evolution governed by nonlinear dispersive PDEs \emph{via} the set of its resonances in an arbitrary big but finite do…
math.PR2017★ 2 cited
Differential equations driven by rough paths with jumps
Peter K. Friz, Huilin Zhang
We develop the rough path counterpart of Itô stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (Itô…
math.PR2015★ 1 cited
A Complex Version of G-Expectation and its Application to Conformal Martingale
Huilin Zhang
This paper is concerned with the connection between G-Brownian Motion and analytic functions. We introduce the complex version of sublinear expectation, and then do the stochastic…