The Pólya Sum Process: Limit Theorems for Conditioned Random Fields

Conditioned Limit Theorems for Random Walks with Negative Drift*

In this paper we will solve a problem posed by Iglehart. In (1975) he conjectured that if Sn is a random walk with negative mean and finite variance then there is a constant c~ so that (St,.j/c~nl/2[N>n) converges weakly to a process which he called the Brownian excursion. It will be shown that his conjecture is false or, more precisely, that if ES~ = a < 0 , ES~ < oo, and there is a slowly var...

Conditioned Limit Theorems for Weighted Sums of Random Sequence

Some notions of conditionally dominated random variables are introduced and characterized, Under rather minimal assumptions on random variables {X,Xn, n ≥ 1}, some limit theorems of Jamison’s type of weighted sums of random variables are obtained. Mathematics Subject Classification: 60F15

Exponential inequalities and functional central limit theorems for random fields

We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform...

Limit theorems for excursion sets of stationary random fields

We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi–, positively or negatively) associated random fields with stochastically continuous realizations for a fixed excursion level. This class includes in particular Gaussian, P...

The Erwin Schrr Odinger International Institute for Mathematical Physics Martingale-diierence Random Fields Limit Theorems and Some Applications Martingale-diierence Random Fields. Limit Theorems and Some Applications