Abstract:
The paper is devoted to a systematic study of the distributions of functionals of stochastic processes by the fibering method and to a survey of results obtained in this direction in recent years. Principal attention is given to distinguishing conditions ensuring: a) absolute continuity; b) the existence of a bounded density; c) applicability of the local limit theorem for the distributions of functionals. Smooth, convex functionals and functionals of integral type are considered in detail.
Citation:
Yu. A. Davydov, M. A. Lifshits, “Fibering method in some probabilistic problems”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 22, VINITI, Moscow, 1984, 61–157; J. Soviet Math., 31:2 (1985), 2796–2858
\Bibitem{DavLif84}
\by Yu.~A.~Davydov, M.~A.~Lifshits
\paper Fibering method in some probabilistic problems
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1984
\vol 22
\pages 61--157
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv59}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=778385}
\zmath{https://zbmath.org/?q=an:0566.60040|0571.60048}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 31
\issue 2
\pages 2796--2858
\crossref{https://doi.org/10.1007/BF02116602}
Linking options:
https://www.mathnet.ru/eng/intv59
https://www.mathnet.ru/eng/intv/v22/p61
This publication is cited in the following 18 articles:
Axel Bücher, Holger Dette, Florian Heinrichs, “Detecting deviations from second-order stationarity in locally stationary functional time series”, Ann Inst Stat Math, 72:4 (2020), 1055
A. N. Borodin, Yu. A. Davydov, V. B. Nevzorov, “On the History of the St. Petersburg School of Probability and Statistics. III. Distributions of Functionals of Processes, Stochastic Geometry, and Extrema”, Vestnik St.Petersb. Univ.Math., 51:4 (2018), 343
Jean-Christophe Breton, “Regularity of the Laws of Shot Noise Series and of Related Processes”, J Theor Probab, 23:1 (2010), 21
Theory Probab. Appl., 51:2 (2007), 256–278
Jean-Christophe Breton, “Absolute Continuity of Joint Laws of Multiple Stable Stochastic Integrals”, J Theor Probab, 18:1 (2005), 43
“Absolute continuity between a Gibbs measure
and its translate”, Theory Probab. Appl., 49:4 (2005), 713–724
Jean-Christophe Breton, “Absolue continuité des lois jointes des intégrales stables multiples”, Comptes Rendus. Mathématique, 334:2 (2002), 135
Emmanuel Nowak, “Distance en variation totale entre une mesure de Gibbs et sa translatée”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:2 (1998), 239
A. M. Nikulin, “The strong convergence of distributions of Brownian sojourn times in procedures of approximations”, J. Math. Sci. (New York), 93:3 (1999), 399–413
V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239
Yu. A. Davydov, R. R. Manukyan, “A local limit theorem for multiple Wiener–Itô stochastic integrals”, Theory Probab. Appl., 40:2 (1995), 354–361
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
V. Paulauskas, A. Račkauskas, “Nonuniform estimates in the central limit theorem in Banach spaces”, Lith Math J, 31:3 (1991), 335
R. Norvaiša, V. Paulauskas, “Rate of convergence in the central limit theorem for empirical processes”, J Theor Probab, 4:3 (1991), 511
V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Russian Math. Surveys, 45:3 (1990), 1–104
V. I. Paulauskas, “A note on Gaussian measure of balls in Banach spaces”, Theory Probab. Appl., 35:4 (1990), 802–805
M. A. Lifshits, “Distribution density of the norm of a stable vector”, J Math Sci, 43:6 (1988), 2810
Yu. A. Davydov, “Absolute continuity of the images of measures”, J. Soviet Math., 36:4 (1987), 468–473
Citation in format AMSBIB
Contact us: