Stochastic differential equations in a scale of Hilbert spaces

Alexei Daletskii

Stochastic differential equations in a scale of Hilbert spaces

Mathematics

Research output: Contribution to journal › Article › peer-review

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 R.

Original language	English
Journal	Electronic Journal of Probability
Publication status	Accepted/In press - 18 Nov 2018

Bibliographical note

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Access to Document

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This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
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Cite this

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title = "Stochastic differential equations in a scale of Hilbert spaces",

abstract = "A stochastic differential equation with coefficients defined in a scale ofHilbert spaces is considered. The existence and uniqueness of finite timesolutions is proved by an extension of the Ovsyannikov method. This resultis applied to a system of equations describing non-equilibrium stochasticdynamics of (real-valued) spins of an infinite particle system on a typicalrealization of a Poisson or Gibbs point process in R.",

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N2 - A stochastic differential equation with coefficients defined in a scale ofHilbert spaces is considered. The existence and uniqueness of finite timesolutions is proved by an extension of the Ovsyannikov method. This resultis applied to a system of equations describing non-equilibrium stochasticdynamics of (real-valued) spins of an infinite particle system on a typicalrealization of a Poisson or Gibbs point process in R.

AB - A stochastic differential equation with coefficients defined in a scale ofHilbert spaces is considered. The existence and uniqueness of finite timesolutions is proved by an extension of the Ovsyannikov method. This resultis applied to a system of equations describing non-equilibrium stochasticdynamics of (real-valued) spins of an infinite particle system on a typicalrealization of a Poisson or Gibbs point process in R.

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SN - 1083-6489

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

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