Stochastic Integration with Respect to Cylindrical Lévy Processes by p-Summing Operators

We introduce a stochastic integral with respect to cylindrical Lévy processes with finite p-th weak moment for $$p\in [1,2]$$p∈[1,2]. The space of integrands consists of p-summing operators between Banach spaces of martingale type p. We apply the developed integration theory to establish the existence of a solution for a stochastic evolution equation driven by a cylindrical Lévy process.

On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations

We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

Statistical Physics of the Inflaton Decaying in an Inhomogeneous Random Environment

We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton probability distribution is derived. The relative entropy (free energy) of the stochastic wave is defined. The second law of thermodynamics for the diffusive system is obtained. Gaussian probability distributions are studied in detail.

Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients S2−almost automorphic

In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S

Large deviations for SPDEs of jump type

In this paper, we establish a large deviation principle for a fully nonlinear stochastic evolution equation driven by both Brownian motions and Poisson random measures on a given Hilbert space H. The weak convergence method plays an important role.