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Stochastic differential equations in a scale of Hilbert spaces. (English) Zbl 1406.60087
Summary: 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 \({\mathbb{R} }^{n}\).
MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
46E99 Linear function spaces and their duals
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