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.
Full text available as:
|PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
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 2000 > 60 Probability theory and stochastic processes|
|Deposited By:||Mrs Louise Healey|
|Deposited On:||19 November 2007|