Thomas M. Lewis

A law of the iterated logarithm for stable processes in random scenery

We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence.

ITERATED BROWNIAN MOTION AND ITS INTRINSIC SKELETAL STRUCTURE

This is an overview of some recent results on the stochastic analysis of iterated Brownian motion. In particular, we make explicit an intrinsic skeletal structure for the iterated Brownian motion which can be thought of as the analogue of the strong Markov property. As a particular application, we derive a change of variables (i.e., Ito’s) formula for iterated Brownian motion.

A law of the iterated logarithm for random walk in random scenery with deterministic normalizers

AbstractLetX, Xi,i≥1, be a sequence of independent and identically distributed ℤd-valued random vectors. LetSo=0 and

On the future infima of some transient processes

S_n = \sum\nolimits_{i = 1}^n {X_i }

Limit theorems for partial sums of quasi-associated random variables

forn≤1. Furthermore letY, Y(α), α∈ℤd, be independent and identically distributed ℝ-valued random variables, which are independent of theXi. Let

The favorite point of a Poisson process

Z_n = \sum\nolimits_{i = 0}^n {Y(S_i )}