In this paper, the authors study a double random integral of the form [integral operator]01[integral operator]01f(s,t) M(ds) M(dt), where M(0,t) is a stable process with independent increments. Basically, the Wiener approach is used, and the existence of the above integral is established for a...

Let ..., X-1, X0, X1, ... be symmetric i.i.d. random variables belonging to the domain of normal attraction of an [alpha]-stable distribution with 1 [alpha] 2, and let cj = j-[beta][Lambda](j) with 1/[alpha] [beta] and a slowly varying [Lambda](j). We study the limit behavior of the partial...

The rate of convergence (in the uniform Kolmogorov's distance) for probability distributions of parabolically rescaled solutions of the multidimensional Burgers' equation with random singular Gaussian initial data (with long-range dependence) to a limit Gaussian random field is discussed in this...