Quadratic functionals of Brownian motion

Takeyuki Hida

Journal of Multivariate Analysis, 1971, vol. 1, issue 1, 58-69

Abstract: Functionals of Brownian motion can be dealt with by realizing them as functionals of white noise. Specifically, for quadratic functionals of Brownian motion, such a realization is a powerful tool to investigate them. There is a one-to-one correspondence between a quadratic functional of white noise and a symmetric L2(R2)-function which is considered as an integral kernel. By using well-known results on the integral operator we can study probabilistic properties of quadratic or certain exponential functionals of white noise. Two examples will illustrate their significance.

Keywords: white; noise; functional; of; Brownian; motion; modified; Fredholm; determinant; semiinvariant; stochastic; area; equivalence; of; Gaussian; measures (search for similar items in EconPapers)
Date: 1971
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