Diffusion approximation for equilibrium Kawasaki dynamics in continuum

Kondratiev Y, Kutoviy OV, Lytvynovd EW (2008)
STOCHASTIC PROCESSES AND THEIR APPLICATIONS 118(7): 1278-1299.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in R-d which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure mu as invariant measure. We study a diffusive limit of such a dynamics, derived through a scaling of both the jump rate and time. Under weak assumptions on the potential of pair interaction, phi, (in particular, admitting a singularity of phi at zero), we prove that, on a set of smooth local functions, the generator of the scaled dynamics converges to the generator of the gradient stochastic dynamics. If the set on which the generators converge is a core for the diffusion generator, the latter result implies the weak convergence of finite-dimensional distributions of the corresponding equilibrium processes. In particular, if the potential phi is from C-b(3) (R-d) and sufficiently quickly converges to zero at infinity, we conclude the convergence of the processes from a result in [V. Choi, Y.M. Park, H.J. Yoo, Dirichlet forms and Dirichlet operators for infinite particle systems: Essential self-adjointness, J. Math. Phys. 39 (1998) 6509-6536]. (C) 2007 Elsevier B.V. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Band
118
Ausgabe
7
Seite(n)
1278-1299
ISSN
PUB-ID

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Kondratiev Y, Kutoviy OV, Lytvynovd EW. Diffusion approximation for equilibrium Kawasaki dynamics in continuum. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 2008;118(7):1278-1299.
Kondratiev, Y., Kutoviy, O. V., & Lytvynovd, E. W. (2008). Diffusion approximation for equilibrium Kawasaki dynamics in continuum. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 118(7), 1278-1299. doi:10.1016/j.spa.2007.09.001
Kondratiev, Y., Kutoviy, O. V., and Lytvynovd, E. W. (2008). Diffusion approximation for equilibrium Kawasaki dynamics in continuum. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 118, 1278-1299.
Kondratiev, Y., Kutoviy, O.V., & Lytvynovd, E.W., 2008. Diffusion approximation for equilibrium Kawasaki dynamics in continuum. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 118(7), p 1278-1299.
Y. Kondratiev, O.V. Kutoviy, and E.W. Lytvynovd, “Diffusion approximation for equilibrium Kawasaki dynamics in continuum”, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 118, 2008, pp. 1278-1299.
Kondratiev, Y., Kutoviy, O.V., Lytvynovd, E.W.: Diffusion approximation for equilibrium Kawasaki dynamics in continuum. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 118, 1278-1299 (2008).
Kondratiev, Yuri, Kutoviy, Oleksandr V., and Lytvynovd, Eugene W. “Diffusion approximation for equilibrium Kawasaki dynamics in continuum”. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 118.7 (2008): 1278-1299.