Conditioned Limit Theorems

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

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...

Total Variation Approximations and Conditional Limit Theorems for Multivariate Regularly Varying Random Walks Conditioned on Ruin

We study a new technique for the asymptotic analysis of heavy-tailed systems conditioned on large deviations events. We illustrate our approach in the context of ruin events of multidimensional regularly varying random walks. Our approach is to study the Markov process described by the random walk conditioned on hitting a rare target set. We construct a Markov chain whose transition kernel can ...

Entropy and Limit Theorems

I hereby declare that my thesis entitled`Entropy and Limit Theo-rems' is not substantially the same as any that I have submitted for a degree or diploma or other qualiication at any other University. I further state that no part of my thesis has already been or is being concurrently submitted for any such degree, diploma or other qualiication. Chapter 3 extends results from a paper co-written w...

Some Limit Theorems