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On the quadratic Wiener functional associated with the Malliavin derivative of the square norm of Brownian sample path on interval. (English) Zbl 1111.60037

Summary: Exact expressions of the stochastic oscillatory integrals with the phase function, which is the quadratic Wiener functional obtained from the Malliavin derivative of the square norm of the Brownian sample path on interval, are given. As an application, the density function of the distribution of the half of the Wiener functional is given.

MSC:

60H07 Stochastic calculus of variations and the Malliavin calculus
60E10 Characteristic functions; other transforms
60E05 Probability distributions: general theory
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