Supercritical branching processes are considered which are Markovian in the age structure but where reproduction parameters may depend upon population size and even the age structure of the population. Such processes generalize Bellman-Harris processes as well as customary demographic processes...

A null recurrent Markov chain is associated with a stationary mixing S[alpha]S process. The resulting process exhibits such strong dependence that its sample covariance grows at a surprising rate which is slower than one would expect based on the fatness of the marginal distribution tails. An...

It is known that if the Lévy measure of a Lévy process X(t), 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1, is "heavy tailed", then the right tails of sup0[less-than-or-equals, slant]t[less-than-or-equals, slant]1X(t) and X(1) are of the same rate of decay. One of the results of...

The reduction method provides an algorithm to compute large deviation estimates of (possibly nonreversible) Markov processes with exponential transition rates. It replaces the original graph minimisation equations of Freidlin and Wentzell by more tractable path minimisation problems. When...

In this paper we solve problems of eigenvalues of stochastic Hamiltonian systems with boundary conditions and construct the corresponding eigenfunctions. This is a sort of forward-backward stochastic differential equations (FBSDE) parameterized by . The problem is to find non-trivial solutions...

The object of this paper is to obtain the multifractal structure for the local time of a general Lévy process which hits points. All such local time measures can be represented as the occupation measure of a subordinator. The thick points in the spectrum were investigated in a recent paper by...

In the time series literature one can often find the claim that the periodogram ordinates of an iid sequence at the Fourier frequencies behave like an iid standard exponential sequence. We review some results about functions of these periodogram ordinates, including the convergence of extremes,...

We find conditions which are sufficient and nearly necessary for the compact and bounded law of the iterated logarithm for Markov chains with a countable state space.

Quantitative geometric rates of convergence for reversible Markov chains are closely related to the spectral gap of the corresponding operator, which is hard to calculate for general state spaces. This article describes a geometric argumen t to give different types of bounds for spectral gaps of...

Let X1,X2,...,Xn be a sample from a stationary Gaussian time series and let I(·) be the sample periodogram. Some researchers have either proved heuristically or claimed that under general conditions, the asymptotic behaviour of is equivalent to that of the discrete version of the integral...