In this article, we present a rigorous mathematical derivation of a macroscopic model of aggregation, scaling up from a microscopic description of a family of individuals subject to aggregation/repulsion, described by a system of Itô type stochastic differential equations. We analyze the asymptotics of the system for both a large number of particles on a bounded time interval, and its long time behavior, for a fixed number of particles. As far as this second part is concerned, we show that a suitable localizing potential is required, in order that the system may admit a nontrivial invariant distribution.

Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions / V. Capasso, D. Morale. - In: STOCHASTIC ANALYSIS AND APPLICATIONS. - ISSN 0736-2994. - 27:3(2009), pp. 574-603.

Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions

V. Capasso
Primo
;
D. Morale
Ultimo
2009

Abstract

In this article, we present a rigorous mathematical derivation of a macroscopic model of aggregation, scaling up from a microscopic description of a family of individuals subject to aggregation/repulsion, described by a system of Itô type stochastic differential equations. We analyze the asymptotics of the system for both a large number of particles on a bounded time interval, and its long time behavior, for a fixed number of particles. As far as this second part is concerned, we show that a suitable localizing potential is required, in order that the system may admit a nontrivial invariant distribution.
Empirical measure; Invariant measure; Law of large numbers; Measure-valued processes; Stochastic differential equations
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/139337
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