We prove that the set of points where exceptional oscillation of lp-valued Gaussian processes occur infinitely often is a random fractal, and evaluate its Hausdorff dimension. Applications to fractional Brownian motions and Ornstein-Uhlenbeck processes are also discussed.

Consider a discrete-time x2-process, i.e. a process defined as the sum of squares of independent and identically distributed Gaussian processes. Count the number of values that exceed a certain level. Let this level and the number of time points considered increase simultaneously so that the...

This paper first proves a sufficient and necessary condition for the right continuity of a family of two-parameter [sigma]-fields. Then, it proceeds to introduce condition (Fs3) and proves that condition (Fs3) is equivalent to right continuity of a family of [sigma]-fields prior to stopping lines.

We consider the stochastic differential equation dXt= b(Xt)dZt, t[greater-or-equal, slanted]o, where b is a Borel measurable real function and Z is a symmetric [alpha]-stable Lévy motion. In Section 1 we study the convergence of certain functionals of Z and in particular, we extend Engelbert...

We analyze the speed of convergence to stationarity for a specific stochastic system consisting of a finite number of interacting particles on the circle. We define a coupling and a martingale related to this coupling to show that the time needed to approach stationarity is a polynomial in the...

We give a general method for finding the long-time asymptotic growth rate of mean occupation times of one-dimensional continuous strong Markov processes. The method uses a well-known decomposition of the resolvent, previous work of Kasahara (1975), and some new comparison results. Particular...

Let X be a super-Brownian motion with a general (time-space) homogeneous branching mechanism. We study a relation between lifetime and compactness of range for X. Under a restricted condition on the branching mechanism, we show that the set X survives is the same as that the range of X is...

In this paper we obtain lower bounds for the tails of the distributions of the first passage-times for some stochastic processes. We consider first discrete parameter processes with asymptotically small drifts taking values in + and prove for them a general result giving lower bounds for these...

In this paper we prove the existence and uniqueness, as well as the regularity, of the adapted solution to a class of degenerate linear backward stochastic partial differential equations (BSPDE) of parabolic type. We apply the results to a class of forward-backward stochastic differential...

Possible definitions of the long range dependence (LRD) of a stationary point process are discussed. Examples from the standard queueing literature are considered and shown to be amenable to yielding processes with long range count dependence. In particular the effect of the single-server...