Asymptotic distributions of continuous-time random walks: A probabilistic approach

Journal Article · Wed Nov 01 00:00:00 EST 1995 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02179257· OSTI ID:468298

Kotulski, M ^[1]

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1. Technical Univ. of Wroclaw (Poland)

We provide a systematic analysis of the possible asymptotic distributions of one-dimensional continuous-time random walks (CTRWs) by applying the limit theorems of probability theory. Biased and unbiased walks of coupled and decoupled memory are considered. In contrast to previous work concerning decoupled memory and Levy walks, we deal also with arbitrary coupled memory and with jump densities asymmetric about its mean, obtaining asymmetric Levy-stable limits. Surprisingly, it is found that in most cases coupled memory has no essential influence on the form of the limiting distribution. We discuss interesting properties of walks with an infinite mean waiting time between successive jumps.

• Sponsoring Organization: USDOE
• OSTI ID: 468298
• Journal Information: Journal of Statistical Physics, Vol. 81, Issue 3-4; Other Information: PBD: Nov 1995
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 MATHEMATICS
COMPUTERS
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MANAGEMENT
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MISCELLANEOUS
STATISTICAL MODELS
ASYMPTOTIC SOLUTIONS
RANDOMNESS
FRACTALS
BOUNDARY CONDITIONS
TURBULENCE
PROBABILITY