First passage time densities for random walk spans

Journal Article · Sat Feb 01 04:00:00 EST 1986 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01127728· OSTI ID:6910780

Weiss, G H; DiMarzio, E A; Gaylord, R J

A general expression is derived for the Laplace transform of the probability density of the first passage time for the span of a symmetric continuous-time random walk to reach level S. The authors show that when the mean time between steps is finite, the mean first passage time to S is proportional to S/sup 2/. When the pausing time density is asymptotic to a stable density the authors show that the first passage density is also asymptotically stable. Finally, when the jump distribution of the random walk has an asymptotic form raised to the negative power alpha plus 1 with alpha restricted between the values of 0 and 2, it is shown that the mean first passage time to S goes like S raised to the corresponding power of alpha.

• Research Organization: NIH, Bethesda, MD
• OSTI ID: 6910780
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 42:3; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
FUNCTIONS
INTEGRAL TRANSFORMATIONS
LAPLACE TRANSFORMATION
MATHEMATICAL MODELS
MECHANICS
PARTICLE MODELS
PARTICLES
RANDOMNESS
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
STRUCTURE FUNCTIONS
TRANSFORMATIONS
TRANSPORT THEORY