Fix a function such that , where d=1, and each function is strictly increasing, right continuous with left limits. We prove the equilibrium fluctuations for exclusion processes with conductances, induced by W, in random environments, when the system starts from an equilibrium measure. The...

The TCP window size process appears in the modeling of the famous transmission control protocol used for data transmission over the Internet. This continuous time Markov process takes its values in [0,[infinity]), and is ergodic and irreversible. It belongs to the additive...

This paper proves that the log-spot in the Heston model has a density and gives an expression of this density as an infinite convolution of Bessel type densities. Such properties are deduced from a factorization of the characteristic function, mainly obtained through an analysis of the complex...

In this study, we consider the exponential utility maximization problem in the context of a jump-diffusion model. To solve this problem, we rely on the dynamic programming principle to express the value process of this problem in terms of the solution of a quadratic BSDE with jumps. Since the...

Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, Skorokhod spaces, Lusin spaces or general topological spaces. Our contributions are twofold: we dramatically...

For an absorbing diffusion X0 on a one dimensional regular interval I with no killing inside, the Dirichlet form of X0 on L2(I;m) and its extended Dirichlet space are identified in terms of the canonical scale s of X0, where m is the canonical measure of X0. All possible symmetric extensions of...

By adopting the coupling method, we obtain new verifiable sufficient conditions about the -Feller continuity, the Lipschitz continuity and the strong Feller continuity of the semigroups associated with Lévy type operators. These results easily apply to jump-diffusion processes and stochastic...

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law...

We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle density converges to the solution of a certain nonlinear...

We study the long time limiting behavior of the occupation time of the superprocess over a stochastic flow introduced by Skoulakis and Adler (2001) [13]. The ergodic theorems for dimensions d=2 and d=3 are established. The proofs depend heavily on a characterization of the conditional...