Band 22, Heft 2

Abstract. We consider stochastic processes from an Orlicz space of random variables. There are obtained estimates for distributions of some functionals from this space. Square Gaussian stochastic processes are investigated in more detail.

Abstract. The aim of this work is to study the existence, uniqueness and exponential stability of mild solutions for some stochastic neutral partial functional integrodifferential equations. We suppose that the linear part has a resolvent operator in the sense given in Grimmer [Transactions of the American Mathematical Society 273 (1982), 333–349]. The nonlinear part is assumed to be continuous and lipschitzian with respect to the second argument. Firstly, we study the existence of mild solutions. Secondly we give some results on the exponential stability in mean square sense. An example is provided to illustrate the results of this work.

Abstract. In this paper we introduce and study a self-similar Gaussian process denoted by SH,K${{S^{H,\,K}}}$ with parameters H∈(0,1)${{H\in (0,1)}}$ and K∈[0,1]${{K\in [0,1]}}$. This process generalizes the well-known fractional Brownian motion introduced by Mandelbrot and Van Ness [SIAM Rev. 10 (1968), no. 4, 422–437], the sub-fractional Brownian motion introduced by Bojdecki, Gorostiza and Talarczyket [Statist. Probab. Lett. 69 (2004), 405–419] and the Gaussian process introduced by Lei and Nualart [Statist. Probab. Lett. 79 (2009), 619–624] in order to obtain a decomposition in law of the bifractional Brownian motion.

Abstract. By using large deviation techniques, we prove a Strassen type law of the iterated logarithm for a forward-backward stochastic differential equation.

Abstract. In this paper we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 1<β≤2$1&lt;\beta \le 2$. Our result is similar to that of Marcus and Rosen in 1992 for local time. The second result is to give a ( p , q )-variation of fractional derivatives of local time of symmetric stable process with index 1<β≤2$1&lt;\beta \le 2$. Our approach is similar to that of Eisenbaum in 2000 for local time.

Abstract. In this work we study Lifshitz tails for Laplacians in a percolation model on ℝd${\mathbb {R}}^d$. At any lattice point i in ℝd${\mathbb {R}}^d$ we remove a set S+i${S+i}$ with a certain probability p . We consider the Laplacian on the remaining subset of ℝd${\mathbb {R}}^d$ with either Dirichlet or Neumann boundary conditions. We prove that the integrated density of states exhibits Lifshitz behavior at the bottom of the spectrum when we consider Dirichlet boundary conditions, while when we consider Neumann boundary conditions, it exhibits a van Hove behavior.

Abstract. We consider a multivalued forward-backward stochastic differential equation where the diffusion coefficient of the forward equation is perturbed by a small parameter ε>0${\varepsilon &gt; 0}$. We prove that, as ε goes to 0, the solution of the backward equation converges to the solution of a deterministic backward equation and satisfies a Freidlin–Wentzell type large deviation principle.