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2018 Stochastic differential equations in a scale of Hilbert spaces
Alexei Daletskii
Electron. J. Probab. 23: 1-15 (2018). DOI: 10.1214/18-EJP247

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

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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

Information

Received: 13 May 2018; Accepted: 18 November 2018; Published: 2018
First available in Project Euclid: 15 December 2018

zbMATH: 07021675
MathSciNet: MR3896856
Digital Object Identifier: 10.1214/18-EJP247

Subjects:
Primary: 60H10
Secondary: ‎46E99, 82C20, 82C31

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Vol.23 • 2018
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