Stochastic differential equations in a scale of Hilbert spaces

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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 R.
Original languageEnglish
JournalElectronic Journal of Probability
Publication statusAccepted/In press - 18 Nov 2018

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