PreprintGaussMarkov processes on Hilbert spacesBen Goldys, Szymon Peszat and Jerzy ZabczykAbstractK. Itô characterized in [13] zeromean stationary Gauss Markovprocesses evolving on a class of infinitedimensional spaces. In this work we extend the work of Itô in the case of Hilbert spaces: GaussMarkov families that are timehomogenous are identified as solutions to linear stochastic differential equations with singular coefficients. Choosing an appropriate locally convex topology on the space of weakly sequentially continuous functions we also characterize the transition semigroup, the generator and its core thus providing an infinitedimensional extension of the classical result of Courrège [3] in the case of GaussMarkov semigroups. Keywords: Gauss–Markov process, Ornstein–Uhlenbeck process, Gaussian measure, bwtopology, strict topology, generator.AMS Subject Classification: Primary 60G15; secondary 60H15, 60J99.
This paper is available as a pdf (396kB) file.
