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: | https://eprints.maths.manchester.ac.uk/id/eprint/909 |
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