We consider the sum X of i.i.d. random variables Yn, n[greater-or-equal, slanted]0, with weights an which decay exponentially fast to zero. For a smooth sublinear increasing function g, g(Y0) has finite expectation if and only if the expectation of Xg'(X) is finite. The proof uses characteristic...

The present paper addresses the situation where the reserve of an insurance business is currently invested in an asset that may yield negative interest. Upper and lower bounds for the probability of ruin are obtained in the case where the cash flow of premiums less claims and the logarithm of...

We consider a transient random walk on in random environment, and study the almost sure asymptotics of the supremum of its local time. Our main result states that if the random walk has zero speed, there is a (random) sequence of sites and a (random) sequence of times such that the walk spends a...

We give necessary and sufficient conditions for geometric and polynomial ergodicity of a Markov chain on the real line with invariant distribution equal to the distribution of the mean of a Dirichlet process with parameter [alpha]. This extends the applicability of a recent MCMC method for...

We establish new Kahane-Khintchine inequalities in Orlicz spaces induced by exponential Young functions for stationary real random fields which are bounded or satisfy some finite exponential moment condition. Next, we give sufficient conditions for partial sum processes indexed by classes of...

An explicit formula is obtained for the prediction error of a future value of a stationary process when the infinite past is altered by some missing observations with an arbitrary pattern. Then the autoregressive representation of the predictor is derived and the processes for which the missing...

Motivated by the work of Tilman (Ecology 75 (1994) 2) and May and Nowak (J. Theoret. Biol. 170 (1994) 95) we consider a process in which points are inserted randomly into the unit interval and a new point kills each point to its left independently and with probability a. Intuitively this dynamic...

We investigate asymptotic properties of two-dimensional empirical point processes of exceedances (EPPE). We give an alternative description of the class of possible limit laws. Necessary and sufficient conditions for the weak convergence of one-dimensional EPPEs and complete convergence of...

We consider the ordinary stochastic differential equation on the closed unit ball E in . While it is easy to prove existence and distribution uniqueness for solutions of this SDE for each c[greater-or-equal, slanted]0, pathwise uniqueness can be proved by standard methods only in dimension n=1...

We use the continuity theorem of Lyons for rough paths in the p-variation topology to produce an elementary approach to the large deviation principle and the support theorem for diffusion processes. The proofs reduce to establish the corresponding results for Brownian motion itself as a rough...