Zhongmin Qian - Academia.edu (original) (raw)

Papers by Zhongmin Qian

Probability Theory and Related Fields

$Research paper thumbnail of Fine properties of fractional Brownian motions on Wiener space$

Journal of Mathematical Analysis and Applications

Journal of the London Mathematical Society

Frontiers of Mathematics in China

Comptes Rendus Mathematique, Dec 1, 2002

... a, Laboratoire de statistique et probabilités CNRS, Université Paul-Sabatier, 118, route de N... more ... a, Laboratoire de statistique et probabilités CNRS, Université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 4, France. ... Amer. Math. Soc., 73 (1967), pp. 890–896. [2] M.Gradinaru, S. Herrmann and B. Roynette, A singular large deviations phenomenon. Ann. Inst. ...

$Research paper thumbnail of Stochastic analysis, rough path analysis and fractional Brownian motions$

Probability Theory and Related Fields, 2002

We derive a non-linear version of the Feynman-Kac formula for the solutions of the vorticity equa... more We derive a non-linear version of the Feynman-Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence (global in time) and uniqueness for a stochastic terminal value problem associated with the vorticity equation in dimension 2.

Eprint Arxiv 1203 3857, Mar 17, 2012

An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochasti... more An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of BSDEs (without involving any algebraic constraint) whose existence of solutions automatically enforces the original algebraic constraint to be satisfied.

Data Revues 1631073x V347i1 2 S1631073x08003270, Jan 20, 2009

Let u→(⋅,t) be a strong solution of the Navier–Stokes equation on 3-dimensional torus T3, and ω→(... more Let u→(⋅,t) be a strong solution of the Navier–Stokes equation on 3-dimensional torus T3, and ω→(⋅,t)=∇×u→(⋅,t) be the vorticity. In this Note we show that‖ω→(⋅,t)‖1+24ν‖u→(⋅,t)‖22 is decreasing in t as long as the solution u→(⋅,t) exists, where ν&gt;0 is the viscosity constant and ‖⋅‖q denotes the Lq-norm. To cite this article: Z. Qian, C. R. Acad. Sci. Paris, Ser. I

Using a generalized curvature-dimension inequality and a new approach, we present a dierential in... more Using a generalized curvature-dimension inequality and a new approach, we present a dierential inequality for an elliptic second order dierential operator acting on distance functions, from which we deduce volume comparison theorems and diameter bounds without the use of the theory of Jacobi fields.

The Annals of Probability, 1996

Lecture Notes in Mathematics, 1995

Mathematical Control and Related Fields, 2015

Lecture Notes in Mathematics, 2012

We derive several new gradient estimates of Aronson-B{\'e}nilan type for positive solutions o... more We derive several new gradient estimates of Aronson-B{\'e}nilan type for positive solutions of porous medium equation and fast diffusion equation on a complete manifold that satisfies the curvature dimension condition

In this paper, we establish several gradient estimates for the positive solution of Porous Medium... more In this paper, we establish several gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques and Forward and Backward Stochastic Differential Equations (FBSDEs).