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

This article is cited in 41 scientific papers (total in 41 papers)

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
Received: 04.04.1995

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
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\paper The Laplace method for probability measures in Banach spaces
\jour Uspekhi Mat. Nauk
\yr 1995
\vol 50
\issue 6(306)
\pages 57--150
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\transl
\jour Russian Math. Surveys
\yr 1995
\vol 50
\issue 6
\pages 1151--1239
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. R. Fatalov, “Large deviations of the $L^p$-norm of a Wiener process with drift”, Math. Notes, 65:3 (1999), 358–364  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  crossref
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  crossref
    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  mathscinet  zmath  isi
    9. V. R. Fatalov, “Large deviations for Gaussian processes in Hölder norm”, Izv. Math., 67:5 (2003), 1061–1079  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  crossref  mathscinet  zmath
    13. V. R. Fatalov, “The Laplace method for small deviations of Gaussian processes of Wiener type”, Sb. Math., 196:4 (2005), 595–620  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. S. Albeverio, S. Mazzucchi, “Generalized Fresnel integrals”, Bulletin des Sciences Mathématiques, 129:1 (2005), 1  crossref
    15. A.B. Dieker, “Extremes of Gaussian processes over an infinite horizon”, Stochastic Processes and their Applications, 115:2 (2005), 207  crossref
    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  mathnet  crossref  mathscinet  zmath  elib  elib
    17. Yuzuru Inahama, “Laplace's method for the laws of heat processes on loop spaces”, Journal of Functional Analysis, 232:1 (2006), 148  crossref
    18. “Letter to the Editors”, Theory Probab Appl, 51:3 (2007), 561  mathnet  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  mathnet  crossref  mathscinet  zmath  isi  elib
    21. V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 157:2 (2008), 1606–1625  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    23. “Introduction”, Mathematical Theory of Feynman Path Integrals: An Introduction, 523 (2008), 1  crossref  mathscinet  isi
    24. V. R. Fatalov, “Exact asymptotics of Laplace-type Wiener integrals for $L^p$-functionals”, Izv. Math., 74:1 (2010), 189–216  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    25. Yuzuru Inahama, “A Stochastic Taylor-Like Expansion in the Rough Path Theory”, J Theoret Probab, 2010  crossref
    26. V. R. Fatalov, “Large deviations for distributions of sums of random variables: Markov chain method”, Problems Inform. Transmission, 46:2 (2010), 160–183  mathnet  crossref  mathscinet  isi  elib
    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  crossref
    28. V. R. Fatalov, “Exact asymptotics of probabilities of large deviations for Markov chains: the Laplace method”, Izv. Math., 75:4 (2011), 837–868  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    30. Zakhar Kabluchko, “Extremes of the standardized Gaussian noise”, Stochastic Processes and their Applications, 121:3 (2011), 515  crossref
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    32. V. R. Fatalov, “Negative-order moments for $L^p$-functionals of Wiener processes: exact asymptotics”, Izv. Math., 76:3 (2012), 626–646  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    35. V. R. Fatalov, “The Laplace method for Gaussian measures and integrals in Banach spaces”, Problems Inform. Transmission, 49:4 (2013), 354–374  mathnet  crossref  isi
    36. V. R. Fatalov, “On the Laplace method for Gaussian measures in a Banach space”, Theory Probab. Appl., 58:2 (2014), 216–241  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    37. FuChang Gao, XiangFeng Yang, “Upper tail probabilities of integrated Brownian motions”, Sci. China Math, 2015  crossref
    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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    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  mathnet  crossref  crossref  adsnasa  isi  elib
    41. V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, Theoret. and Math. Phys., 195:2 (2018), 641–657  mathnet  crossref  crossref  adsnasa  isi  elib
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