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Stationary measures of stochastic gradient systems, infinite lattice models

  • J. Fritz
Article

Summary

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.

Keywords

Stochastic Process Stability Condition Probability Theory Stationary Measure Interaction Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

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

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