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Self attracting diffusions: Two case studies. (English) Zbl 0838.60052

There are given two typical examples where the self attractiveness implies convergence and scalar functional stochastic differential equations in the general model of it.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:

[1] M. Cranston, T.S. Mountford, The Strong Law of Large Numbers for a Brownian Polymer, To appear, Annals of Probability · Zbl 0873.60014
[2] R. Durrett, L.C.G. Rogers, A symptotic behavior of Brownian polymers, Prob. Theory Rel. Fields,92, 337-349, 1991 · Zbl 0767.60080 · doi:10.1007/BF01300560
[3] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland, New York, 1981 · Zbl 0495.60005
[4] M. Ledoux, M. Talagrand, Probability in Banach spaces: isoperimetry and processes. Springer-Verlag, New York, 1991 · Zbl 0748.60004
[5] J.R. Norris, L.C.G. Rogers, D. Williams, Self-avoiding random walk: a Brownian motion model with local time drift, Prob. Theory Rel. Fields,74, 271-287, 1987 · Zbl 0611.60052 · doi:10.1007/BF00569993
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