Electronic Journal of Probability

Stochastic differential equations in a scale of Hilbert spaces

Alexei Daletskii

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1544843299

Digital Object Identifier
doi:10.1214/18-EJP247

Mathematical Reviews number (MathSciNet)
MR3896856

Zentralblatt MATH identifier
07021675

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10] 46E99: None of the above, but in this section

Keywords
stochastic differential equation scale of Hilbert spaces infinite particle system

Rights
Creative Commons Attribution 4.0 International License.

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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