Stochastic differential equations in a scale of Hilbert spaces. Global solutions.

Georgy Chargaziya; Alex Daletskii

doi:10.1214/23-ECP557

Stochastic differential equations in a scale of Hilbert spaces. Global solutions.

Georgy Chargaziya, Alex Daletskii

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, uniqueness and path-continuity of infinite-time solutions are proved by an extension of the Ovsyannikov method. These results are 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 n . The paper improves the results of the work by the second named author "Stochastic differential equations in a scale of Hilbert spaces", Electron. J. Probab. 23, where finite-time solutions were constructed.

Original language	English
Article number	ECP557
Number of pages	13
Journal	Electronic Communications in Probability
Volume	28
DOIs	https://doi.org/10.1214/23-ECP557
Publication status	Published - 14 Nov 2023

Access to Document

10.1214/23-ECP557Licence: CC BY

23-ECP557Final published version, 379 KBLicence: CC BY

Cite this

@article{18132ce41c7d4db895dacb5619dfd25d,

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

abstract = "A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions are proved by an extension of the Ovsyannikov method. These results are 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 n . The paper improves the results of the work by the second named author {"}Stochastic differential equations in a scale of Hilbert spaces{"}, Electron. J. Probab. 23, where finite-time solutions were constructed.",

author = "Georgy Chargaziya and Alex Daletskii",

year = "2023",

month = nov,

day = "14",

doi = "10.1214/23-ECP557",

language = "English",

volume = "28",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Stochastic differential equations in a scale of Hilbert spaces. Global solutions.

AU - Chargaziya, Georgy

AU - Daletskii, Alex

PY - 2023/11/14

Y1 - 2023/11/14

N2 - A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions are proved by an extension of the Ovsyannikov method. These results are 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 n . The paper improves the results of the work by the second named author "Stochastic differential equations in a scale of Hilbert spaces", Electron. J. Probab. 23, where finite-time solutions were constructed.

AB - A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions are proved by an extension of the Ovsyannikov method. These results are 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 n . The paper improves the results of the work by the second named author "Stochastic differential equations in a scale of Hilbert spaces", Electron. J. Probab. 23, where finite-time solutions were constructed.

U2 - 10.1214/23-ECP557

DO - 10.1214/23-ECP557

M3 - Article

SN - 1083-589X

VL - 28

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

M1 - ECP557

ER -