We consider a class of stochastic evolution models for particles diffusing on a lattice and interacting by creation-annihilation processes. The particle number at each site is unbounded. We prove that in the macroscopic (continuum) limit the particle density satisfies a reaction-diffusion PDE, and that microscopic fluctuations around the average are described by a generalized Omstein-Uhlenbeck process, for which the covariance kernel is explicitely exhibit
Non-equilibrium fluctuations in particle systems modelling diffusion-reaction equations / Boldrighini, Carlo; DE MASI, A.; Pellegrinotti, A.. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 42:(1992), pp. 1-30. [10.1016/0304-4149(92)90023-J]
Non-equilibrium fluctuations in particle systems modelling diffusion-reaction equations
BOLDRIGHINI, Carlo;
1992
Abstract
We consider a class of stochastic evolution models for particles diffusing on a lattice and interacting by creation-annihilation processes. The particle number at each site is unbounded. We prove that in the macroscopic (continuum) limit the particle density satisfies a reaction-diffusion PDE, and that microscopic fluctuations around the average are described by a generalized Omstein-Uhlenbeck process, for which the covariance kernel is explicitely exhibitI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
