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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].

##### MSC:
 60H07 Stochastic calculus of variations and the Malliavin calculus