23 citations · 99 across the 56 of their papers we have counts for
5 papers · 2 filters
On the Finite Dimensional Joint Characteristic Function of Lévy's Stochastic Area Processes
Xi Geng, Zhongmin Qian
The goal of this paper is to derive a formula for the finite dimensional joint characteristic function (the Fourier transform of the finite dimensional distribution) of the coupled…
Gradient estimates for porous medium and fast diffusion equations by martingale method
Ying Hu, Zhongmin Qian, Zichen Zhang
In this paper, we establish several local and global gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof i…
Quasi-sure convergence theorem in -variation distance for stochastic differential equations
H. Boedihardjo, Z. Qian
In this paper by calculating carefully the capacities (defined by high order Sobolev norms on the Wiener space) for some functions of Brownian motion, we show that the dyadic appro…
A Note on Indefinite Stochastic Riccati Equations
Zhongmin Qian, Xun Yu Zhou
An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness co…
BMO Martingales and Positive Solutions of Heat Equations
Ying Hu, Zhongmin Qian
In this paper, we develop a new approach to establish gradient estimates for positive solutions to the heat equation of elliptic or subelliptic operators on Euclidean spaces or on…