## Abstract

It is shown that if φ(f) ∝_{Rd} φ(y) f(y) dy is a Markoff random field and X_{α} are multiplicative functionals of φ (with E(X_{α}) = 1) which converge locally in L_{1}, then there exists a locally Markoff random field φ_{*} such that E(exp(iφ_{*}(f))) = lim_{α} E(X_{α} exp(iφ(φ))). We choose φ to be the two-dimensional generalization of the Ornstein-Uhlenbeck velocity process and take X_{α} proportional to exp(-λ∝_{R2} : P(φ(y)) : g_{α}(y) dy), where: P(φ(y)) : is a regularized even degree polynomial in φ(y). It is then proved that for an appropriate choice of g_{α} → 1 and small λ, {X_{α}} does converge locally in L_{1} and that the corresponding φ_{*} is stationary.

Original language | English (US) |
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Pages (from-to) | 44-61 |

Number of pages | 18 |

Journal | Journal of Functional Analysis |

Volume | 14 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1973 |

## ASJC Scopus subject areas

- Analysis