Martingales, Tauberian Theorem, and Strategies of Gambling

DOI10.1137/S0040585X9797571XzbMath0895.60047MaRDI QIDQ4384404

Alexander Novikov

Publication date: 8 September 1998

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

zbMATH Keywords

optimal stoppinguniform integrabilitysharp inequalitieslocal martingalesWald equationboundary crossing problemgambling strategies

Mathematics Subject Classification ID

Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40)

Related Items (14)

First-passage times for random walks with nonidentically distributed increments ⋮ On the First-Passage Time of a Diffusion Process Over a One-Sided Stochastic Boundary ⋮ Crossing an asymptotically square-root boundary by the Brownian motion ⋮ Curve crossing for random walks reflected at their maximum ⋮ The first passage time problem over a moving boundary for asymptotically stable Lévy processes ⋮ On distibutions of first passage times of martingales arising in some gambling problems ⋮ Weak tail conditions for local martingales ⋮ The Kolmogorov Inequality for the Maximum of the Sum of Random Variables and Its Martingale Analogues ⋮ First Passage Problems over Increasing Boundaries for Lévy Processes with Exponentially Decayed Lévy Measures ⋮ On the first-passage times of certain Gaussian processes, and related asymptotics ⋮ The tail estimation of the quadratic variation of a quasi left continuous local martingale ⋮ Asymptotics of first-passage time over a one-sided stochastic boundary ⋮ Derivative martingale of the branching Brownian motion in dimension \(d\ge 1\) ⋮ Limit at Zero of the First-Passage Time Density and the Inverse Problem for One-Dimensional Diffusions

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