An Invariance Principle for Parabolic SPDEs

Abstract

Throughout this chapter we suppose that J₁, J₂, $\ldots$ are independent, identically distributed random variables, with values in $\mathbb{Z}$, and assume that there exist constants $\kappa, \alpha\;>0$ such that the characteristic function $\phi$ of the J_i’s satisfies

$$\phi(z) := Ee^{izJ_{1}}=\;1-\kappa |Z|^{\alpha}\;+\;o(|z|^{\alpha}) \;\mathrm{as}\;z\rightarrow0$$

.