22 citations · 61 across the 10 of their papers we have counts for
10 papers
Classical solution of path-dependent mean-field semilinear PDEs
Shanjian Tang, Huilin Zhang
The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which…
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1
Alexey Korepanov, Zemer Kosloff, Ian Melbourne
We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_…
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…
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2
Ilya Chevyrev, Peter K. Friz, Alexey Korepanov +2
We consider deterministic homogenization for discrete-time fast-slow systems of the form …
Exponential mixing for dissipative PDEs with bounded non-degenerate noise
Sergei Kuksin, Huilin Zhang
We prove that well posed quasilinear equations of parabolic type, perturbed by bounded nondegenerate random forces, are exponentially mixing for a large class of random forces.
Multiscale systems, homogenization, and rough paths
Ilya Chevyrev, Peter K. Friz, Alexey Korepanov +2
In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classi…
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…
Wong-Zakai Approximation for SDEs Driven by Brownian Motion
Shige Peng, Huilin Zhang
In this paper, we build the equivalence between rough differential equations driven by the lifted -Brownian motion and the corresponding Stratonovich type SDE through the Wong-Z…
Stochastic Calculus with respect to G-Brownian Motion Viewed through Rough Paths
Shige Peng, Huilin Zhang
In this paper, we study rough path properties of stochastic integrals of Itô's type and Stratonovich's type with respect to -Brownian motion. The roughness of -Brownian Motio…
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…