dorsal/arxiv
View SchemaVariable Step Random Walks and Self-Similar Distributions
| Authors | Gemunu H. Gunaratne, Joseph L. McCauley, Matthew Nicol, Andrei Torok |
|---|---|
| Categories | |
| ArXiv ID | physics/0412182 |
| URL | https://arxiv.org/abs/physics/0412182 |
| DOI | 10.1007/s10955-005-5474-y |
Abstract
We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the theorem implies that the scaling index $\zeta$ is 1/2. For corresponding continuous time processes, it is shown that the probability density function $W(x;t)$ satisfies the Fokker-Planck equation. Possible forms for the diffusion coefficient are given, and related to $W(x,t)$. Finally, we show how a time-series can be used to distinguish between these variable diffusion processes and L\'evy dynamics.
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"abstract": "We study a scenario under which variable step random walks give anomalous\nstatistics. We begin by analyzing the Martingale Central Limit Theorem to find\na sufficient condition for the limit distribution to be non-Gaussian. We note\nthat the theorem implies that the scaling index $\\zeta$ is 1/2. For\ncorresponding continuous time processes, it is shown that the probability\ndensity function $W(x;t)$ satisfies the Fokker-Planck equation. Possible forms\nfor the diffusion coefficient are given, and related to $W(x,t)$. Finally, we\nshow how a time-series can be used to distinguish between these variable\ndiffusion processes and L\\\u0027evy dynamics.",
"arxiv_id": "physics/0412182",
"authors": [
"Gemunu H. Gunaratne",
"Joseph L. McCauley",
"Matthew Nicol",
"Andrei Torok"
],
"categories": [
"physics.data-an",
"physics.flu-dyn"
],
"doi": "10.1007/s10955-005-5474-y",
"title": "Variable Step Random Walks and Self-Similar Distributions",
"url": "https://arxiv.org/abs/physics/0412182"
},
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