An infinite dimensional stochastic differential equation with state spaceC(ℝ)

Abstract

We consider a time evolution of unbounded continuous spins on the real line. The evolution is described by an infinite dimensional stochastic differential equation with local interaction. Introducing a condition which controls the growth of paths at infinity, we can construct a diffusion process taking values inC(ℝ). In view of quantum field theory, this is a time dependent model ofP(φ)1 field in Parisi and Wu's scheme.