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Exponential Convergence for a System of Conuclear Space-Valued Diffusions with Mean-Field Interaction

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Abstract.

We consider an interacting system of n diffusion processes X n j (t): t∈[0,1] , j=1,2,. . ., n , taking values in a conuclear space Φ' . Let ζn t =(1/n)Σ n j=1 δ Xnj(t) be the empirical process. It has been proved that ζ n , as n→∞ , converges to a deterministic measure-valued process which is the unique solution of a nonlinear differential equation. In this paper we show that, under suitable conditions, ζ n converges to ζ at an exponential rate.

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Authors and Affiliations

  1. Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, USA jxiong@math.utk.edu, , , , , , US

    J. Xiong

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  1. J. Xiong
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Accepted 20 October 1997

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Xiong, J. Exponential Convergence for a System of Conuclear Space-Valued Diffusions with Mean-Field Interaction. Appl Math Optim 39, 281–307 (1999). https://doi.org/10.1007/s002459900107

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  • DOI: https://doi.org/10.1007/s002459900107

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