Generalized gambler's ruin problem: explicit formulas via Siegmund duality

DOI10.1007/s11009-016-9507-6zbMath1370.60120arXiv1604.05990OpenAlexW2340999293WikidataQ59608332 ScholiaQ59608332MaRDI QIDQ2397967

Paweł Lorek

Publication date: 14 August 2017

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.05990

zbMATH Keywords

Markov chainspartial orderingMöbius monotonicityabsorption probabilitySiegmund dualitygeneralized gambler's ruin problem

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Stopping times; optimal stopping problems; gambling theory (60G40) Probabilistic games; gambling (91A60)

Related Items (9)

Antiduality and Möbius monotonicity: generalized coupon collector problem ⋮ SIEGMUND DUALITY FOR MARKOV CHAINS ON PARTIALLY ORDERED STATE SPACES ⋮ Susceptible-exposed-infectious model using Markov chains ⋮ Harmonic numbers in gambler's ruin problem ⋮ Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model ⋮ Unnamed Item ⋮ Deciding when to quit the gambler's ruin game with unknown probabilities ⋮ Explicit transient probabilities of various Markov models ⋮ The exponential-dual matrix method: Applications to Markov chain analysis

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