Submultiplicative moments of the supremum of a random walk with negative drift

DOI10.1016/S0167-7152(96)00097-1zbMath0903.60055MaRDI QIDQ1380548

Mikhail S. Sgibnev

Publication date: 5 January 1999

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

Wiener-Hopf factorizationrandom walkinfinite divisibility

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Multiplicative functionals and Markov processes (60J57)

Related Items (18)

Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation ⋮ Stone’s decomposition of the renewal measure via Banach-algebraic techniques ⋮ Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk ⋮ A Lundberg-type inequality for an inhomogeneous renewal risk model ⋮ A general method for finding the optimal threshold in discrete time ⋮ A two-sided bound for the renewal function when the interarrival distribution is IMRL ⋮ Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes ⋮ Wiener-Hopf equation whose kernel is a probability distribution ⋮ Uniform asymptotics of the finite-time ruin probability for all times ⋮ On Stone's renewal theorem for arithmetic distributions ⋮ On the inhomogeneous conservative Wiener-Hopf equation ⋮ Asymptotic expansion of the solution of a differential-difference equation of general form ⋮ Asymptotics of solutions of an integro-differential and an integral equation ⋮ Asymptotics of solutions of matrix integro-differential equations ⋮ Asymptotic expansion of the solution of an integro-differential equation with exact asymptotics of the remainder ⋮ Asymptotic behaviour of the finite-time ruin probability in renewal risk models ⋮ Matrix Volterra integral equation with submultiplicative asymptotics of the inhomogeneous term ⋮ The discrete Wiener-Hopf equation with submultiplicative asymptotics of the solution

Cites Work

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• Banach algebras of measures on the line
• On convolution tails
• On generalized renewal measures and certain first passage times
• Asymptotic behaviour of Wiener-Hopf factors of a random walk
• On the Characteristics of the General Queueing Process, with Applications to Random Walk
• Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift

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