Stationary measures of stochastic gradient systems, infinite lattice models

  • J. Fritz


Let G be the formal generator of a d-dimensional stochastic gradient system associated to an interaction potential U. If ∫ G ϕ d μ= 0 for such smooth ϕ that G ϕ IL1(μ), then certain moment conditions imply that μ is a Gibbs random field for U. If U satisfies a stability condition, and d≦2 or μ is translation invariant, then these moment conditions can be replaced by a natural support condition. Results of Holley and Stroock [6] are extended to certain unbounded spin systems.


Stochastic Process Stability Condition Probability Theory Stationary Measure Interaction Potential 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J. Fritz
    • 1
  1. 1.Mathematical InstituteBudapestHungary

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