Predicting the last zero of Brownian motion with drift

DOI10.1080/17442500701840950zbMath1145.60025arXiv0712.3415OpenAlexW2116733708MaRDI QIDQ3498585

Goran Peskir, Albert N. Shiryaev, Jacques Du Toit

Publication date: 15 May 2008

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3415

zbMATH Keywords

optimal stoppingBrownian motionoptimal predictionsmooth fitparabolic free-boundary problemlast zero

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Inference from stochastic processes and prediction (62M20) Other nonlinear integral equations (45G10) Brownian motion (60J65) Stopping times; optimal stopping problems; gambling theory (60G40) Free boundary problems for PDEs (35R35) Prediction theory (aspects of stochastic processes) (60G25)

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Cites Work

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• The trap of complacency in predicting the maximum
• A change-of-variable formula with local time on curves
• Stopping Brownian Motion Without Anticipation as Close as Possible to Its Ultimate Maximum
• On a Property of the Moment at Which Brownian Motion Attains Its Maximum and Some Optimal Stopping Problems
• Heuristic Approach to the Kolmogorov-Smirnov Theorems
• On Certain Confidence Contours for Distribution Functions

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