NDLI: Persistence of integrated stable processes

Content Provider	Springer Nature Link
Author	Profeta, Christophe Simon, Thomas
Copyright Year	2014
Abstract	We compute the persistence exponent of the integral of a stable Lévy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Shi (Lower tails of some integrated processes. In: Small deviations and related topics (problem panel 2003). Along the way, we investigate the law of the stable process $$L$$ evaluated at the first time its integral $$X$$ hits zero, when the bivariate process $$(X,L)$$ starts from a coordinate axis. This extends classical formulæ by McKean (J Math Kyoto Univ 2:227–235, 1963) and Gor’kov (Soviet. Math. Dokl. 16:904–908, 1975) for integrated Brownian motion.
Ending Page	485
Page Count	23
Starting Page	463
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	3
Volume Number	162
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-07-30
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hitting place Mathematical and Computational Biology Theoretical, Mathematical and Computational Physics Probability Theory and Stochastic Processes Lower tail probability Quantitative Finance Integrated process Persistence Stable Lévy process Statistics for Business/Economics/Mathematical Finance/Insurance Operations Research/Decision Theory Half-Cauchy distribution Stable processes Boundary theory Mellin transform
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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