Let B(t) be a Brownian motion on R, B(0) = 0, and for [alpha]n:= 2-n let Tn0 = 0, Tnk+1 = inf{t Tnk:B(t)-B(Tnk) = [alpha]n}, 0 [less-than-or-equals, slant] k. Then B(Tnk):= Rn(k[alpha]2n) is the nth approximating random walk. Define Mn by TnMn = T(-1) (the passage time to -1) and let L(x) be the...

Let denote the set of functions f(t,x) which are [alpha]-Hölder continuous in t and 2[alpha]-Hölder continuous in x. For 0 [alpha] 1/4 we prove a large deviation principle in a separable subset of for the solution X[var epsilon][phi](t,x) to a parabolic stochastic partial differential...

The problems of designing the efficient sampling designs for estimation of random fields by piecewise constant estimators are studied, which is done asymptotically, namely, as the sample size goes to infinity. The performance of sampling designs is measured by the integrated mean-square error....

We study stochastic forced oscillations of a mass-spring system with time-dependent, stochastic damping. The main purpose is to analyze the effect of the time-dependent damping. The oscillations are governed by the second-order stochastic differential equation , where x denotes the motion, Wt...

This paper studies the approximation of the density Pt,x(y) of the solution of the nonlinear limit-problem of a system of weakly interacting SDE's via a convolution of the empirical measure of the system with a family of smooth mollifiers. The method, which mainly uses coupling techniques and...

In this paper, a new algorithm of simulated annealing is suggested. It is shown that this algorithm gives more rapid convergence than the usual algorithm. A logarithmic Sobolev inequality is also established.

In this paper, it is shown that the Wentzell-Freidlin large deviations estimates for random evolution equations still hold with the sup-norm replaced by any Hölder norm with exponent .

In this paper we show that the solution of a second-order stochastic differential equation with diffusion coefficient and boundary conditions X0 = 0 and X1 = 1 is a 2-Markov field if and only if the drift is a linear function. The proof is based on the method of change of probability and makes...

Consider a p-variate counting process N = (N(i)) with jump times {[tau](i)1, [tau](i)2, ...}. Suppose that the intensity of jumps [lambda](i) of N(i) at time t depends on the time since its last jump as well as on the times since the last jumps of the other components, i.e. [lambda](i)(t) =...

We prove an extension of Itô's formula for F(Xt, t), where F(x, t) has a locally square integrable derivative in x that satisfies a mild continuity condition in t, and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying some properties. Following the ideas...