Tusheng Zhang

Convergence of non-symmetric dirichlet processes

In this paper we study the limit behaviour of the diffusion processes generated by non-divergence operators and prove that the diffusion processes converge weakly when the corresponding coefficients converge

Generalized Feynman–Kac Semigroups, Associated Quadratic Forms and Asymptotic Properties

AbstractIn this paper, we study the Feynman–Kac semigroup Ttf(x)=Ex[f(Xt)exp(Nt)],where Xt is a symmetric Levy process and Nt is a continuous additive functional of zero energy which is not necessarily of bounded variation. We identify the corresponding quadratic form and obtain large time asymptotics of the semigroup. The Dirichlet form theory plays an important role in the whole paper.

Approximation of arbitrary Dirichlet processes by Markov chains

Abstract We prove that any Hunt process on a Hausdorff topological space associated with a Dirichlet form can be approximated by a Markov chain in a canonical way. This also gives a new proof for the existence of Hunt processes associated with strictly quasi-regular Dirichlet forms on general state spaces.

Large Deviations for Stochastic Models of Two-Dimensional Second Grade Fluids

In this paper, we establish a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by Budhiraja and Dupuis (Probab Math Statist 20:39–61, 2000) plays an important role.

PROBABILISTIC REPRESENTATIONS AND HYPERBOUND ESTIMATES FOR SEMIGROUPS

In this paper, we study lower order perturbations of a symmetric second-order differential operator generating a hypercontractive semigroup. We give a probabilistic representation of the, in general, not sub-Markovian semigroup associated with the perturbed operator and prove that the perturbed semigroup is also hypercontractive under some exponential integrability conditions on the coefficients.