Abstract
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a system of equations describing non-equilibrium stochastic dynamics of (real-valued) spins of an infinite particle system on a typical realization of a Poisson or Gibbs point process in ${\mathbb{R} }^{n}$.
Citation
Alexei Daletskii. "Stochastic differential equations in a scale of Hilbert spaces." Electron. J. Probab. 23 1 - 15, 2018. https://doi.org/10.1214/18-EJP247
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