A change of scale formula for Wiener integrals of cylinder functions on the abstract Wiener space II

Young Sik Kim

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 25, 1-7

Abstract:

We show that for certain bounded cylinder functions of the form F ( x ) = μ ˆ ( ( h 1 , x ) ∼ , ... , ( h n , x ) ∼ ) , x ∈ B where μ ˆ : ℝ n → ℂ is the Fourier-transform of the complex-valued Borel measure μ on ℬ ( ℝ n ) , the Borel σ -algebra of ℝ n with ‖ μ ‖ < ∞ , the analytic Feynman integral of F exists, although the analytic Feynman integral, lim z → − i q I a w ( F ; z ) = lim z → − i q ( z / 2 π ) n / 2 ∫ ℝ n f ( u → ) exp { − ( z / 2 ) | u → | 2 } d u → , do not always exist for bounded cylinder functions F ( x ) = f ( ( h 1 , x ) ∼ , ... , ( h n , x ) ∼ ) , x ∈ B . We prove a change of scale formula for Wiener integrals of F on the abstract Wiener space.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:804515

DOI: 10.1155/S0161171201004537

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