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Stochastic Analysis on (Infinite-Dimensional) Product Manifolds

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Stochastic Dynamics

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Abstract

We give a review of our results related to stochastic analysis on product manifolds (infinite products of compact Riemannian manifolds). We introduce differentiable structures on product manifolds and prove the existence and uniqueness theorem for stochastic differential equations on them. This result is applied to the construction of Glauber dynamics for classical lattice models with compact spin spaces. We discuss the relations between ergodicity of the dynamics and extremality of the corresponding Gibbs measures. Further, we construct the associated stochastic dynamics in the space of macroscopic fluctuations of our system.

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Authors
  1. Sergio Albeverio
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  2. Alexei Daletskii
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  3. Yuri Kondratiev
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Albeverio, S., Daletskii, A., Kondratiev, Y. (1999). Stochastic Analysis on (Infinite-Dimensional) Product Manifolds. In: Stochastic Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-22655-9_15

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  • DOI: https://doi.org/10.1007/0-387-22655-9_15

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98512-1

  • Online ISBN: 978-0-387-22655-2

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