It is shown that the blockwise bootstrap of the empirical process for a stationary [beta]-mixing sequences, indexed by VC-subgraph classes of functions, converges weakly to the appropriate Gaussian process, conditionally in probability. The conditions imposed are only marginally stronger than...

We study a model on the non-negative half line +0, {0, 1, 2, ...} in which particles created at the origin at rate 1 jump to the right at rate 1. If a particle jumps onto an already occupied site the two particles annihilate each other. In addition, whenever a particle jumps its closest neighbor...

We consider a broad class of continuous martingales whose local modulus of continuity is in some sense deterministic. We show that such martingales have Gaussian probability tails, provided we appropriately normalize them by their quadratic variation. As other applications of our methods, we...

It is shown that [varrho]([lambda]) = (1 - [lambda]c/[lambda])(2[lambda]2 + 3[lambda] + 2)/(([lambda]2 + [lambda])(1 + [lambda]c)), where [lambda]c is the critical value and [varrho]([lambda]) is the order of the one-dimensional contact process with parameter [lambda]. An implication of this...

We prove a simulated annealing result for stochastic evolution equations on Hilbert spaces. As examples can serve: a class of nonlinear heat equations on C0[0, 1] subject to a decreasing white noise forcing term, and the equations of stochastic plates subject to an evolution of the...

We obtain extreme value limit distributions of the maximum of standardized partial sums of stationary Gaussian random variables with long-range dependence.

A class of processes with a time varying spectral representation is established. As an example we study time varying autoregressions. Several results on the asymptotic norm behaviour and trace behaviour of covariance matrices of such processes are derived. As a consequence we prove a Kolmogorov...

We consider the problem of approximating the distribution of a Markov chain with 'rare' transitions in an arbitrary state space by that of the corresponding pseudo-Poisson process. Sharp estimates for both first- and second-order approximations are obtained. The remarkable fact is that the...

A Polya-like urn arises in studying stationary distributions and stationary sampling distributions in neutral (Fleming-Viot) genetics models with bounded mutation rates. This paper gives a detailed analysis of asymptotic properties of the urn. In particular, it is shown that in a sample of size...

In this paper we derive an alternative representation for the reflection of a continuous, bounded variation process. Under stationarity assumptions we prove a continuous counterpart of Little's law of classical queueing theory. These results, together with formulas from Palm calculus, are used...