On the support of Wiener functionals. (English) Zbl 0790.60047

Elworthy, K. D. (ed.) et al., Asymptotic problems in probability theory: Wiener functionals and asymptotics. Proceedings of the 26th Taniguchi international symposium, Sanda and Kyoto, Japan, August 31 - September 5, 1990. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 284, 3-34 (1993).
Let \((B,H,\mu)\) denote an abstract Wiener space and \(\Phi\) a function from \(B\) to a Polish space \(E\). The authors give a criterion for determining the support in \(E\) of the induced measure \(\mu\circ\Phi^{- 1}\). In the case where \(E\) is a Euclidean space and the induced measure has a continuous density \(f\), they apply this result to study the support of \(f\). In the final section, the results of the previous sections are applied to diffusion processes.
For the entire collection see [Zbl 0780.00029].


60H07 Stochastic calculus of variations and the Malliavin calculus