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An infinite dimensional stochastic differential equation with state spaceC(ℝ)
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  • Published: March 1987

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

  • Koichiro Iwata1 

Probability Theory and Related Fields volume 74, pages 141–159 (1987)Cite this article

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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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Authors and Affiliations

  1. Department of Applied Physics, Tokyo Institute of Technology, Oh-Okayama, Meguro, 152, Tokyo, Japan

    Koichiro Iwata

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  1. Koichiro Iwata
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Cite this article

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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  • Received: 07 November 1985

  • Issue Date: March 1987

  • DOI: https://doi.org/10.1007/BF01845644

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Keywords

  • Differential Equation
  • Field Theory
  • Time Evolution
  • Quantum Field Theory
  • Stochastic Process
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