RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Uspekhi Mat. Nauk: Year: Volume: Issue: Page: Find

 Uspekhi Mat. Nauk, 1995, Volume 50, Issue 6(306), Pages 57–150 (Mi umn1122)

The Laplace method for probability measures in Banach spaces

V. I. Piterbarg, V. R. Fatalov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full text: PDF file (910 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1995, 50:6, 1151–1239

Bibliographic databases:

UDC: 519.2
MSC: 44A10, 35J05, 60B05, 46B09, 28C20, 60J65

Citation: V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Uspekhi Mat. Nauk, 50:6(306) (1995), 57–150; Russian Math. Surveys, 50:6 (1995), 1151–1239

Citation in format AMSBIB
\Bibitem{PitFat95} \by V.~I.~Piterbarg, V.~R.~Fatalov \paper The Laplace method for probability measures in Banach spaces \jour Uspekhi Mat. Nauk \yr 1995 \vol 50 \issue 6(306) \pages 57--150 \mathnet{http://mi.mathnet.ru/umn1122} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1379077} \zmath{https://zbmath.org/?q=an:0871.46020} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995RuMaS..50.1151P} \transl \jour Russian Math. Surveys \yr 1995 \vol 50 \issue 6 \pages 1151--1239 \crossref{https://doi.org/10.1070/RM1995v050n06ABEH002635} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UR75000002} 

• http://mi.mathnet.ru/eng/umn1122
• http://mi.mathnet.ru/eng/umn/v50/i6/p57

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. P. Maslov, A. M. Chebotarev, “Logarithmic asymptotics of solutions of the large deviation problem for the Boltzmann equation with small transfer of momentum”, Math. Notes, 64:1 (1998), 63–81
2. V. R. Fatalov, “Large deviations of the $L^p$-norm of a Wiener process with drift”, Math. Notes, 65:3 (1999), 358–364
3. S. ALBEVERIO, V. STEBLOVSKAYA, “ASYMPTOTICS OF INFINITE-DIMENSIONAL INTEGRALS WITH RESPECT TO SMOOTH MEASURES I”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 02:04 (1999), 529
4. V. M. Khametov, “Asymptotics of the Solution to the Cauchy Problem for Linear Parabolic Equations of Second Order with Small Diffusion”, Math. Notes, 68:6 (2000), 775–789
5. Sergio Albeverio, Haio Röckle, Steblovskaya Victoria, “Asymptotic expansions for Ornstein–Uhlenbeck semigroups perturbed by potentials over Banach spaces”, Stochastics and Stochastic Reports, 69:3-4 (2000), 195
6. A. P. Trifonov, A. V. Zakharov, E. V. Pronyaev, “Adaptive Detection of a Stochastic Signal under Parametric a priori Uncertainty”, Problems Inform. Transmission, 38:3 (2002), 203–217
7. V. R. Fatalov, “Precise Laplace-type asymptotics for moderate deviations of the distributions of sums of independent Banach-valued random elements”, Theory Probab. Appl., 48:4 (2004), 642–663
8. V. R. Fatalov, “Asymptotics of Large Deviations for Wiener Random Fields in Lp-Norm, Nonlinear Hammerstein Equations, and High-Order Hyperbolic Boundary-Value Problems”, Theory Probab Appl, 47:4 (2003), 623
9. V. R. Fatalov, “Large deviations for Gaussian processes in Hölder norm”, Izv. Math., 67:5 (2003), 1061–1079
10. V. R. Fatalov, “Constants in the asymptotics of small deviation probabilities for Gaussian processes and fields”, Russian Math. Surveys, 58:4 (2003), 725–772
11. V. R. Fatalov, “Asymptotics of large deviations of Gaussian processes of Wiener type for $L^p$-functionals, $p>0$, and the hypergeometric function”, Sb. Math., 194:3 (2003), 369–390
12. V. R. Fatalov, “Point Asymptotics for Probabilities of Large Deviations of the $\omega^2$ Statistics in Verification of the Symmetry Hypothesis”, Problems Inform. Transmission, 40:3 (2004), 212–225
13. V. R. Fatalov, “The Laplace method for small deviations of Gaussian processes of Wiener type”, Sb. Math., 196:4 (2005), 595–620
14. S. Albeverio, S. Mazzucchi, “Generalized Fresnel integrals”, Bulletin des Sciences Mathématiques, 129:1 (2005), 1
15. A.B. Dieker, “Extremes of Gaussian processes over an infinite horizon”, Stochastic Processes and their Applications, 115:2 (2005), 207
16. V. R. Fatalov, “Exact Asymptotics of Large Deviations of Stationary Ornstein–Uhlenbeck Processes for $L^p$-Functional, $p>0$”, Problems Inform. Transmission, 42:1 (2006), 46–63
17. Yuzuru Inahama, “Laplace's method for the laws of heat processes on loop spaces”, Journal of Functional Analysis, 232:1 (2006), 148
18. “Letter to the Editors”, Theory Probab Appl, 51:3 (2007), 561
19. V. R. Fatalov, “Occupation times and exact asymptotics of small deviations of Bessel processes for $L^p$-norms with $p>0$”, Izv. Math., 71:4 (2007), 721–752
20. V. R. Fatalov, “Exact Asymptotics of Distributions of Integral Functionals of the Geometric Brownian Motion and Other Related Formulas”, Problems Inform. Transmission, 43:3 (2007), 233–254
21. V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 157:2 (2008), 1606–1625
22. V. R. Fatalov, “Occupation Time and Exact Asymptotics of Distributions of $L^p$-Functionals of the Ornstein–Uhlenbeck Processes, $p>0$”, Theory Probab. Appl., 53:1 (2009), 13–36
23. “Introduction”, Mathematical Theory of Feynman Path Integrals: An Introduction, 523 (2008), 1
24. V. R. Fatalov, “Exact asymptotics of Laplace-type Wiener integrals for $L^p$-functionals”, Izv. Math., 74:1 (2010), 189–216
25. Yuzuru Inahama, “A Stochastic Taylor-Like Expansion in the Rough Path Theory”, J Theoret Probab, 2010
26. V. R. Fatalov, “Large deviations for distributions of sums of random variables: Markov chain method”, Problems Inform. Transmission, 46:2 (2010), 160–183
27. J.B.. Lasserre, E.S.antillan Zeron, “L p -Norms, Log-Barriers and Cramer Transform in Optimization”, Set-Valued Anal, 18:3-4 (2010), 513
28. V. R. Fatalov, “Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method”, Izv. Math., 75:4 (2011), 837–868
29. V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149
30. Zakhar Kabluchko, “Extremes of the standardized Gaussian noise”, Stochastic Processes and their Applications, 121:3 (2011), 515
31. V. R. Fatalov, “Integral Functionals for the Exponential of the Wiener Process and the Brownian Bridge: Exact Asymptotics and Legendre Functions”, Math. Notes, 92:1 (2012), 79–98
32. V. R. Fatalov, “Negative-order moments for $L^p$-functionals of Wiener processes: exact asymptotics”, Izv. Math., 76:3 (2012), 626–646
33. V. R. Fatalov, “Perturbation theory series in quantum mechanics: Phase transition and exact asymptotic forms for the expansion coefficients”, Theoret. and Math. Phys., 174:3 (2013), 360–385
34. V. R. Fatalov, “Ergodic means for large values of $T$ and exact asymptotics of small deviations for a multi-dimensional Wiener process”, Izv. Math., 77:6 (2013), 1224–1259
35. V. R. Fatalov, “The Laplace method for Gaussian measures and integrals in Banach spaces”, Problems Inform. Transmission, 49:4 (2013), 354–374
36. V. R. Fatalov, “On the Laplace method for Gaussian measures in a Banach space”, Theory Probab. Appl., 58:2 (2014), 216–241
37. FuChang Gao, XiangFeng Yang, “Upper tail probabilities of integrated Brownian motions”, Sci. China Math, 2015
38. V. R. Fatalov, “Exact Laplace-type asymptotic formulas for the Bogoliubov Gaussian measure: The set of minimum points of the action functional”, Theoret. and Math. Phys., 191:3 (2017), 870–885
39. V. R. Fatalov, “Brownian motion on $[0,\infty)$ with linear drift, reflected at zero: exact asymptotics for ergodic means”, Sb. Math., 208:7 (2017), 1014–1048
40. V. R. Fatalov, “Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes: exact asymptotics for $L^p$-functionals”, Izv. Math., 82:2 (2018), 377–406
41. V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, Theoret. and Math. Phys., 195:2 (2018), 641–657
•  Number of views: This page: 583 Full text: 191 References: 40 First page: 3