Sufficient conditions for almost surely asymptotic stability with a certain decay function of sample paths, which are given by mild solutions to a class of semilinear stochastic evolution equations, are presented. The analysis is based on introducing approximating system with strong solution and...

For the observation model "signal + white Gaussian noise", an on-line tracking algorithm for signal and its derivatives is proposed. The tracking algorithm applies to a class of signals with derivative up to the kth order. The asyptotic optimality in the minimax sense, with respect to small...

Markov chains have been frequently used to characterize uncertainty in many real-world problems. Quite often, these Markov chains can be decomposed into a vector consisting of fast and slow components; these components are coupled through weak and strong interactions. The main goal of this work...

The model under consideration is a catalytic branching model constructed in Dawson and Fleischmann (1997), where the catalysts themselves undergo a spatial branching mechanism. The key result is a convergence theorem in dimension d = 3 towards a limit with full intensity (persistence), which, in...

The estimation of the multivariate probability density functions f(x1, ... , xd), d = 1, of a stationary random process {Xi} using wavelet methods is considered. Uniform rates of almost sure convergence over compact subsets of d for densities in the Besov space Bspq are established for strongly...

We study the distribution of the stochastic integral [integral operator][infinity]0e-RtdPt where P and R are independent Lévy processes with a finite number of jumps on finite time intervals. The exact distribution is obtained in many special cases, and we derive asymptotic properties of the...

A moderate deviation principle and a Strassen-type law of the iterated logarithm for the small-time propagation of super-Brownian motion are derived. Moderate deviation estimates which are uniform with respect to the starting point are developed in order to prove the law of the iterated...

Let (X1, Y1), (X2, Y2),..., (Xn, Yn) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The...

By proving Chibisov-O'Reilly-type theorems for uniform empirical and quantile processes based on stationary observations, we establish a nonparametric large sample estimation theory for total time on test transforms. In particular, we obtain weak approximations for total time on test transforms...

In this paper we investigate the problem of parametric estimation for multidimensional linear autonomous homogeneous stochastic differential equations. We prove the Local Asymptotical Normality (LAN) property, find the Maximum Likelihood Estimator (MLE), and prove an asymptotical efficiency of...