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Summary

In Chapter 3 we consider (right) transient Markov chains taking values in R. We are interested in down-crossing probabilities for them. These clearly depend on the asymptotic properties of the chain drift at infinity.

This text examines Markov chains whose drift tends to zero at infinity, a topic sometimes labelled as 'Lamperti's problem'. It can be considered a subcategory of random walks, which are helpful in studying stochastic models like branching processes and queueing systems. Drawing on Doob's h-transform and other tools, the authors present novel results and techniques, including a change-of-measure technique for near-critical Markov chains. The final chapter presents a range of applications where these special types of Markov chains occur naturally, featuring a new risk process with surplus-dependent premium rate. This will be a valuable resource for researchers and graduate students working in probability theory and stochastic processes.

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3 - Down-Crossing Probabilities for Transient Markov Chain

Summary

Markov Chains with Asymptotically Zero Drift

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2 results

3 - Down-Crossing Probabilities for Transient Markov Chain

Summary

Markov Chains with Asymptotically Zero Drift