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.
|Titolo:||Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions|
CAPASSO, VINCENZO (Primo)
MORALE, DANIELA (Ultimo)
|Parole Chiave:||Empirical measure; Invariant measure; Law of large numbers; Measure-valued processes; Stochastic differential equations|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2009|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1080/07362990902844421|
|Appare nelle tipologie:||01 - Articolo su periodico|