Electronic Journal of Probability

Stochastic differential equations in a scale of Hilbert spaces

Alexei Daletskii

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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

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

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

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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

stochastic differential equation scale of Hilbert spaces infinite particle system

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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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