On the equivalence of the static and dynamic points of view for diffusions in a random environment
| Autor: | Tom Schmitz |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Harmonic coordinates Stochastic process Applied Mathematics Mathematical analysis Function (mathematics) Covariance Topology Dimension (vector space) Law of large numbers Modelling and Simulation Modeling and Simulation Almost linear coordinates Invariant measure Invariant measures Equivalence (measure theory) Diffusion in a random environment Environment viewed from the particle Mathematics |
| Zdroj: | Stochastic Processes and their Applications. 119:2501-2522 |
| ISSN: | 0304-4149 |
| DOI: | 10.1016/j.spa.2008.12.008 |
| Popis: | We study the equivalence of the static and dynamic points of view for diffusions in a random environment in dimension one. First we prove that the static and dynamic distributions are equivalent if and only if either the speed in the law of large numbers does not vanish, or b / a is a.s. the gradient of a stationary function, where a and b are the covariance coefficient resp. the local drift attached to the diffusion. We moreover show that the equivalence of the static and dynamic points of view is characterized by the existence of so-called “almost linear coordinates”. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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