## Electronic Journal of Probability

### Stochastic differential equations in a scale of Hilbert spaces

Alexei Daletskii

#### 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 ${\mathbb{R} }^{n}$.

#### Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 119, 15 pp.

Dates
Accepted: 18 November 2018
First available in Project Euclid: 15 December 2018

https://projecteuclid.org/euclid.ejp/1544843299

Digital Object Identifier
doi:10.1214/18-EJP247

Mathematical Reviews number (MathSciNet)
MR3896856

Zentralblatt MATH identifier
07021675

#### Citation

Daletskii, Alexei. Stochastic differential equations in a scale of Hilbert spaces. Electron. J. Probab. 23 (2018), paper no. 119, 15 pp. doi:10.1214/18-EJP247. https://projecteuclid.org/euclid.ejp/1544843299

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