Monotone Stochastic Recursions and their Duals

DOI10.1017/S0269964800004137zbMath1095.60519OpenAlexW2099279708MaRDI QIDQ5485351

Karl Sigman, Soren Asmussen

Publication date: 30 August 2006

Published in: Probability in the Engineering and Informational Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0269964800004137

Mathematics Subject Classification ID

Special processes (60K99) Markov processes (60J99)

Related Items (18)

Risk and duality in multidimensions ⋮ Asymptotic behaviour of ancestral lineages in subcritical continuous-state branching populations ⋮ Comparing backwards and forwards random walk maxima ⋮ Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates ⋮ A non-increasing Lindley-type equation ⋮ Generalized gambler's ruin problem: explicit formulas via Siegmund duality ⋮ Sensitivity of the stability bound for ruin probabilities to claim distributions ⋮ Unnamed Item ⋮ On the notion(s) of duality for Markov processes ⋮ On queues with service and interarrival times depending on waiting times ⋮ Loss Rate Asymptotics in aGI/G/1 Queue with Finite Buffer ⋮ Transformations of Galton-Watson processes and linear fractional reproduction ⋮ Lévy Processes with Two-Sided Reflection ⋮ Strong stability in a two-dimensional classical risk model with independent claims ⋮ Rank-dependent Galton‒Watson processes and their pathwise duals ⋮ A multidimensional ruin problem and an associated notion of duality ⋮ Finite-buffer queues with workload-dependent service and arrival rates ⋮ Loss rates in the single-server queue with complete rejection

Cites Work

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• A sample path proof of the duality for stochastically monotone Markov processes
• Stationary random processes associated with point processes
• The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes
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• Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains
• On the Ruin Problem of Collective Risk Theory
• Ruin probabilities expressed in terms of storage processes
• The Recurrence Classification of Risk and Storage Processes
• Stationary distributions for fluid flow models with or without brownian noise
• Ruin probabilities via local adjustment coefficients
• A new look at the Moran dam
• Stochastically monotone Markov Chains

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