## 2007.165: Solutions of affine stochastic functional differential equations in the state space

2007.165:
Markus Riedle
(2007)
*Solutions of affine stochastic functional differential equations in the state space.*

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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 |
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Subjects: | MSC 2000 > 60 Probability theory and stochastic processes |

MIMS number: | 2007.165 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 19 November 2007 |

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