In this paper we consider a position-velocity Ornstein-Uhlenbeck process in an external gradient force field pushing it toward a smoothly imbedded submanifold of R-d, M. The force is chosen so that M is asymptotically stable for the associated deterministic flow. We examine the asymptotic behavior of the system when the force intensity diverges together with the diffusion and the damping coefficients, with appropriate speed. We prove that, under some natural conditions on the initial data, the sequence of position processes is relatively compact, any limit process is constrained on M, and satisfies an explicit stochastic differential equation which, for compact M, has a unique solution.

Calzolari, A., Marchetti, F. (1997). Limit motion of an Ornstein-Uhlenbeck particle on the equilibrium manifold of a force field. JOURNAL OF APPLIED PROBABILITY, 34(4), 924-938.

Limit motion of an Ornstein-Uhlenbeck particle on the equilibrium manifold of a force field

CALZOLARI, ANTONELLA;
1997-12-01

Abstract

In this paper we consider a position-velocity Ornstein-Uhlenbeck process in an external gradient force field pushing it toward a smoothly imbedded submanifold of R-d, M. The force is chosen so that M is asymptotically stable for the associated deterministic flow. We examine the asymptotic behavior of the system when the force intensity diverges together with the diffusion and the damping coefficients, with appropriate speed. We prove that, under some natural conditions on the initial data, the sequence of position processes is relatively compact, any limit process is constrained on M, and satisfies an explicit stochastic differential equation which, for compact M, has a unique solution.
dic-1997
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Con Impact Factor ISI
Diffusions on manifolds; Ornstein-uhlenbeck particle;Constraints; Weak convergence; Convergence of stochastic integrals
Calzolari, A., Marchetti, F. (1997). Limit motion of an Ornstein-Uhlenbeck particle on the equilibrium manifold of a force field. JOURNAL OF APPLIED PROBABILITY, 34(4), 924-938.
Calzolari, A; Marchetti, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/41240
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