Abstract:
It is proved that the distributions of integral-type functionals of diffusion processes and Gaussian random fields are smooth. Exponential estimates are obtained for certain infinite-dimensional oscillatory integrals.
Citation:
V. I. Bogachev, “Functionals of random processes and infinite-dimensional oscillatory integrals connected with them”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 235–266
\Bibitem{Bog92}
\by V.~I.~Bogachev
\paper Functionals of random processes and infinite-dimensional oscillatory integrals connected with them
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 2
\pages 235--266
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\crossref{https://doi.org/10.1070/IM1993v040n02ABEH002166}
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Linking options:
https://www.mathnet.ru/eng/im946
https://doi.org/10.1070/IM1993v040n02ABEH002166
https://www.mathnet.ru/eng/im/v56/i2/p243
This publication is cited in the following 6 articles:
V. I. Bogachev, E. D. Kosov, S. N. Popova, “On distributions of homogeneous and convex functions in Gaussian random variables”, Izv. Math., 85:5 (2021), 852–882
V. I. Bogachev, “Chebyshev–Hermite polynomials and distributions of polynomials in Gaussian random variables”, Theory Probab. Appl., 66:4 (2022), 550–569
P. A. Borodin, I. A. Ibragimov, B. S. Kashin, V. V. Kozlov, A. V. Kolesnikov, S. V. Konyagin, E. D. Kosov, O. G. Smolyanov, N. A. Tolmachev, D. V. Treshchev, A. V. Shaposhnikov, S. V. Shaposhnikov, A. N. Shiryaev, A. A. Shkalikov, “Vladimir Igorevich Bogachev (on his 60th birthday)”, Russian Math. Surveys, 76:6 (2021), 1149–1157
V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Russian Math. Surveys, 71:4 (2016), 703–749
V. I. Bogachev, “Differentiable measures and the Malliavin calculus”, Journal of Mathematical Sciences (New York), 87:4 (1997), 3577
V. I. Bogachev, “Gaussian measures on linear spaces”, Journal of Mathematical Sciences (New York), 79:2 (1996), 933
Citation in format AMSBIB
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