Summary.
Let η be a diffusion process taking values on the infinite dimensional space T Z, where T is the circle, and with components satisfying the equations dη i =σ i (η) dW i +b i (η) dt for some coefficients σ i and b i , i∈Z. Suppose we have an initial distribution μ and a sequence of times t n →∞ such that lim n →∞μS tn =ν exists, where S t is the semi-group of the process. We prove that if σ i and b i are bounded, of finite range, have uniformly bounded second order partial derivatives, and inf i ,ησ i (η)>0, then ν is invariant.
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Received: 12 September 1996 / In revised form: 10 November 1997
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Ramírez, A. Relative entropy and mixing properties of infinite dimensional diffusions. Probab Theory Relat Fields 110, 369–395 (1998). https://doi.org/10.1007/s004400050152
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DOI: https://doi.org/10.1007/s004400050152
- Mathematics Subject Classification (1991): 60K35
- 60J60