Interacting diffusion systems over Z d

Tokuzo Shiga
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Tokuzo Shiga: Tokyo Institute of Technology, Department of Applied Physics

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 311-326 from Springer

Abstract: Summary Interacting diffusion systems are a class of diffusion processes taking values in an infinite product space of an interval, which models the variety of phenomena in physics and biology. This paper surveys the subject of interacting diffusion systems and related problems. Topics include: 1. Introduction. 2. Stationary distributions and ergodic theorems in transient case. 3. Z d -shift invariance of stationary distributions. 4. Local extinction in transient case. 5. Uniformity and local extinction in recurrent case. 6. Parabolic Anderson model and sample Lyapunov exponent. 7. Finite systems of interacting diffusions. 8. Approximation of infinite systems via finite systems. 9. Methods and some technicalities. 9.1 Duality. 9.2 Comparison. 9.3 Coupling. 9.4 Liouville property. 9.5 Random walk estimates. 9.6 Moments estimates. 9.7 Idea of the proof of the approximation result.

Keywords: Random Walk; Stationary Distribution; Ergodic Theorem; Local Extinction; Infinite System (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68532-6_20

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DOI: 10.1007/978-4-431-68532-6_20

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