Abstract.
We show that the set of stationary weak solutions for a class of infinite dimensional stochastic differential equations coincides with the set of shift invariant, space-time Gibbs fields for a certain potential. The key step consists in proving the Gibbs variational principle for space-time Gibbs fields.
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Received: 20 May 1999 / Revised version: 14 May 2001 / Published online: 11 December 2001
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Pra, P., Roelly, S. & Zessin, H. A Gibbs variational principle in space-time for infinite-dimensional diffusions. Probab Theory Relat Fields 122, 289–315 (2002). https://doi.org/10.1007/s004400100170
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DOI: https://doi.org/10.1007/s004400100170
Keywords
- Differential Equation
- Weak Solution
- Variational Principle
- Stochastic Differential Equation
- Gibbs Field