Solutions of affine stochastic functional differential equations in the state space

Riedle, Markus (2007) Solutions of affine stochastic functional differential equations in the state space. [MIMS Preprint]

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Abstract

differential equations on Rd. The drift of these equations is specified by a functional defined on a general function space B which is only described axiomatically. The solutions are reformulated as stochastic processes in the space B. By representing such a process in the bidual space of B we establish that the transition functions of this process form a generalized Gaussian Mehler semigroup on B. Thus the process is characterized completely on B since it is Markovian. Moreover we derive a sufficient and necessary condition on the underlying space B such that the transition functions are even an Ornstein-Uhlenbeck semigroup. We exploit this result to associate a Cauchy problem in the function space B to the finite-dimensional functional equation.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Ms Lucy van Russelt
Date Deposited: 19 Nov 2007
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/909

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