Summary
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.
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Iwata, K. An infinite dimensional stochastic differential equation with state spaceC(ℝ). Probab. Th. Rel. Fields 74, 141–159 (1987). https://doi.org/10.1007/BF01845644
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DOI: https://doi.org/10.1007/BF01845644