A stochastic evolution equation arising from the fluctuations of a class of interacting particle systems
In an earlier paper, we studied the approximation of solutions V (t) to a class of SPDEs by
the empirical measure V n (t) of a system of n interacting diffusions. In the present paper, we
consider a central limit type problem, showing that\sqrt {n}(V nV) n converges weakly, in the
dual of a nuclear space, to the unique solution of a stochastic evolution equation. Analogous
results in which the di. usions that determine V n are replaced by their Euler approximations
are also discussed.
the empirical measure V n (t) of a system of n interacting diffusions. In the present paper, we
consider a central limit type problem, showing that\sqrt {n}(V nV) n converges weakly, in the
dual of a nuclear space, to the unique solution of a stochastic evolution equation. Analogous
results in which the di. usions that determine V n are replaced by their Euler approximations
are also discussed.
Abstract
In an earlier paper, we studied the approximation of solutions V(t) to a class of SPDEs by the empirical measure Vn(t) of a system of n interacting diffusions. In the present paper, we consider a central limit type problem, showing that \sqrt{n}(Vn-V )n converges weakly, in the dual of a nuclear space, to the unique solution of a stochastic evolution equation. Analogous results in which the di.usions that determine Vn are replaced by their Euler approximations are also discussed.
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