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Generalized analytic Feynman integral via function space integral of bounded cylinder functionals. (English) Zbl 1230.60084
The authors define for a generalized Brownian motion process [the first two authors and D. Skoug, Rocky Mt. J. Math. 40, No. 3, 761–788 (2010; Zbl 1202.60133)] a generalized analytic Feynman integral. Then, they obtain some results for the analytic Feynman integral of bounded cylinder functionals, i.e., functionals of the form \[ F(x) = \widehat\nu\big((g_1,x)^\sim, \ldots (g_n,x)^\sim\big), \] where \(x\in C_{a,b}[0,T]\) and with orthonormal elements \(g_1,\ldots, g_n\) from the dual \(C'_{a,b}[0,T]\) [loc. cit.]. The paper also contains a change-of-scale formula for function space integrals of such cylinder functionals.

MSC:
60J65 Brownian motion
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
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