Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks

Details Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks

2004-07-08

arxiv.org/abs/math/0407140v1

Annals of Probability 2004, Vol. 14, No. 3, 1202-1241

Mathematics

Probability

Scientific paper

10.1214/105051604000000260

Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that {(X_n,S_n),n\geq0} is a Markov random walk. In this paper, we prove a uniform Markov renewal theorem with an estimate on the rate of convergence. This result is applied to boundary crossing problems for {(X_n,S_n),n\geq0}. To be more precise, for given b\geq0, define the stopping time \tau=\tau(b)=inf{n:S_n>b}. When a drift \mu of the random walk S_n is 0, we derive a one-term Edgeworth type asymptotic expansion for the first passage probabilities P_{\pi}{\tau

Affiliated with

Also associated with

No associations

Rating

Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform Markov Renewal Theory and Ruin Probabilities in Markov Random Walks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-222526