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Volumn 2, Issue 4, 1999, Pages 529-556

Asymptotics of infinite-dimensional integrals with respect to smooth measures

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EID: 0033264452     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/s021902579900031x     Document Type: Article
Times cited : (14)

References (48)
  • 2
    • 43949175740 scopus 로고
    • Finite-dimensional approach to oscillatory integrals and stationary phase in infinite dimensions
    • S. Albeverio and Z. Brzeźniak, Finite-dimensional approach to oscillatory integrals and stationary phase in infinite dimensions, J. Funct. Anal. 113 (1993) 177-244.
    • (1993) J. Funct. Anal. , vol.113 , pp. 177-244
    • Albeverio, S.1    Brzeźniak, Z.2
  • 3
    • 0346798770 scopus 로고
    • Diffusion fields, quantum fields and fields with values in groups
    • Stochastic Analysis and Applications, ed. M. Pinsky (Marcel Dekker)
    • S. Albeverio and R. Høegh-Krohn, Diffusion fields, quantum fields and fields with values in groups, in Stochastic Analysis and Applications, Adv. in Probability, ed. M. Pinsky (Marcel Dekker, 1984), pp. 1-98.
    • (1984) Adv. in Probability , pp. 1-98
    • Albeverio, S.1    Høegh-Krohn, R.2
  • 4
    • 0011261328 scopus 로고
    • Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics, I
    • S. Albeverio and R. Høegh-Krohn, Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics, I, Invent. Math. 40 (1977) 59-106.
    • (1977) Invent. Math. , vol.40 , pp. 59-106
    • Albeverio, S.1    Høegh-Krohn, R.2
  • 5
    • 0011357346 scopus 로고
    • Feynman path integrals and the corresponding method of stationary phase
    • Proceedings, Marseille International Colloquium on Mathematical Problems in Feynman Path Integrals, May 1978, eds. S. Albeverio, Ph. Combe, R. Høegh-Krohn, G. Rideau, M. Sirugue-Collin and R. Stora, Springer
    • S. Albeverio and R. Høegh-Krohn, Feynman path integrals and the corresponding method of stationary phase, in Proceedings, Marseille International Colloquium on Mathematical Problems in Feynman Path Integrals, May 1978, eds. S. Albeverio, Ph. Combe, R. Høegh-Krohn, G. Rideau, M. Sirugue-Collin and R. Stora, Lecture Notes in Physics, Vol. 106 (Springer, 1979), pp. 3-57.
    • (1979) Lecture Notes in Physics , vol.106 , pp. 3-57
    • Albeverio, S.1    Høegh-Krohn, R.2
  • 10
    • 0347248018 scopus 로고    scopus 로고
    • Asymptotic expansions for Ornstein-Uhlenbeck semigroups perturbed by potentials over Banach spaces
    • S. Albeverio, H. Röckle and V. Steblovskaya, Asymptotic expansions for Ornstein-Uhlenbeck semigroups perturbed by potentials over Banach spaces, to appear in Stochastics Stochastics Rep.
    • Stochastics Stochastics Rep.
    • Albeverio, S.1    Röckle, H.2    Steblovskaya, V.3
  • 11
    • 12144280222 scopus 로고
    • Integrals of rapidly oscillating functions and singularities of the projections of Lagrange manifolds
    • Russian
    • V. Arnol'd, Integrals of rapidly oscillating functions and singularities of the projections of Lagrange manifolds, Funct. Anal. Its Appl. 6 (1972) 61-62 (Russian).
    • (1972) Funct. Anal. Its Appl. , vol.6 , pp. 61-62
    • Arnol'd, V.1
  • 14
    • 0001579803 scopus 로고
    • Méthode de Laplace et de la phase stationnaire sur l'espace de Wiener
    • G. Bénarous, Méthode de Laplace et de la phase stationnaire sur l'espace de Wiener, Stochastics 25 (1988) 125-153.
    • (1988) Stochastics , vol.25 , pp. 125-153
    • Bénarous, G.1
  • 15
    • 84934656350 scopus 로고
    • Intégrales Exponentielles
    • Springer-Verlag
    • E. Combet, Intégrales Exponentielles, Lecture Notes in Math., Vol. 937 (Springer-Verlag, 1982).
    • (1982) Lecture Notes in Math. , vol.937
    • Combet, E.1
  • 19
    • 84980151353 scopus 로고
    • Asymptotic evaluation of certain Markov process expectations for large time
    • M. Donsker and S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time. III, Comm. Pure Appl. Math. 29 (1976) 389-461. Also in: Probabilistic Methods in the Study of Asymptotics, Lecture Notes in Math., Vol. 1427 (Springer, 1991).
    • (1976) III, Comm. Pure Appl. Math. , vol.29 , pp. 389-461
    • Donsker, M.1    Varadhan, S.2
  • 20
    • 84980151353 scopus 로고
    • Probabilistic Methods in the Study of Asymptotics
    • Springer
    • M. Donsker and S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time. III, Comm. Pure Appl. Math. 29 (1976) 389-461. Also in: Probabilistic Methods in the Study of Asymptotics, Lecture Notes in Math., Vol. 1427 (Springer, 1991).
    • (1991) Lecture Notes in Math. , vol.1427
  • 22
    • 84980174402 scopus 로고
    • Oscillatory integrals, Lagrange immersions and unfolding of singularities
    • J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math. 27 (1974) 207-281.
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 207-281
    • Duistermaat, J.1
  • 23
    • 0001329024 scopus 로고
    • On the Morse index in variational calculus
    • J. Duistermaat, On the Morse index in variational calculus, Adv. Math. 21 (1976) 173-195.
    • (1976) Adv. Math. , vol.21 , pp. 173-195
    • Duistermaat, J.1
  • 25
    • 84968466875 scopus 로고
    • Asymptotic analysis of Gaussian integrals. I. Isolated minimum points
    • R. Ellis and J. Rosen, Asymptotic analysis of Gaussian integrals. I. Isolated minimum points, Trans. Amer. Math. Soc. 273 (1982) 447-481.
    • (1982) Trans. Amer. Math. Soc. , vol.273 , pp. 447-481
    • Ellis, R.1    Rosen, J.2
  • 30
    • 0003401596 scopus 로고
    • Introduction to the Theory of Linear Non-self-adjoint Operators
    • AMS
    • I. Gohberg and M. Krein, Introduction to the Theory of Linear Non-self-adjoint Operators, Transl. Math. Monographs, Vol. 24 (AMS, 1970).
    • (1970) Transl. Math. Monographs , vol.24
    • Gohberg, I.1    Krein, M.2
  • 32
    • 84966217285 scopus 로고
    • Homogeneous chaos, p-forms, scaling and the Feynman integral
    • G. W. Johnson and G. Kallianpur, Homogeneous chaos, p-forms, scaling and the Feynman integral, Trans. Amer. Math. Soc. 340 (1993) 503-548.
    • (1993) Trans. Amer. Math. Soc. , vol.340 , pp. 503-548
    • Johnson, G.W.1    Kallianpur, G.2
  • 33
    • 0347248017 scopus 로고
    • Freidlin-Wentzel type estimates for abstract Wiener spaces
    • G. Kallianpur and H. Oodaira, Freidlin-Wentzel type estimates for abstract Wiener spaces, Sankhya Ser. A40 (1978) 116-137.
    • (1978) Sankhya Ser. , vol.A40 , pp. 116-137
    • Kallianpur, G.1    Oodaira, H.2
  • 35
    • 0347248013 scopus 로고
    • Precise estimate for large deviation of Donsker-Varadhan type
    • S. Kusuoka and Y. Tamura, Precise estimate for large deviation of Donsker-Varadhan type, J. Fac. Sci. Univ. Tokyo, Sec. IA, Math. 38 (1991) 533-565.
    • (1991) J. Fac. Sci. Univ. Tokyo, Sec. IA, Math. , vol.38 , pp. 533-565
    • Kusuoka, S.1    Tamura, Y.2
  • 36
    • 0001912992 scopus 로고
    • Precise asymptotics of certain Wiener functionals
    • S. Kusuoka and D. Stroock, Precise asymptotics of certain Wiener functionals, J. Funct. Anal. 99 (1991) 1-74.
    • (1991) J. Funct. Anal. , vol.99 , pp. 1-74
    • Kusuoka, S.1    Stroock, D.2
  • 37
    • 0010786497 scopus 로고
    • Extension holomorphe des fonctionnelles analytiques définies sur un espace de Wiener réel, formule de Cauchy, phase stationnaire
    • P. Malliavin and S. Taniguchi, Extension holomorphe des fonctionnelles analytiques définies sur un espace de Wiener réel, formule de Cauchy, phase stationnaire, C. R. Acad. Sci. 322 (1966) 261-265.
    • (1966) C. R. Acad. Sci. , vol.322 , pp. 261-265
    • Malliavin, P.1    Taniguchi, S.2
  • 38
    • 0031065706 scopus 로고    scopus 로고
    • Analytic functions, Cauchy formula, and stationary phase on a real abstract Wiener space
    • P. Malliavin and S. Taniguchi, Analytic functions, Cauchy formula, and stationary phase on a real abstract Wiener space, J. Funct. Anal. 143 (1997) 470-528.
    • (1997) J. Funct. Anal. , vol.143 , pp. 470-528
    • Malliavin, P.1    Taniguchi, S.2
  • 39
    • 0345987024 scopus 로고    scopus 로고
    • Asymptotics of oscillatory integrals with quadratic phase function on Wiener space
    • D. Nualart and V. Steblovskaya, Asymptotics of oscillatory integrals with quadratic phase function on Wiener space, Stochastics Stochastics Rep. 66 (1999) 293-309.
    • (1999) Stochastics Stochastics Rep. , vol.66 , pp. 293-309
    • Nualart, D.1    Steblovskaya, V.2
  • 41
    • 84968507607 scopus 로고
    • Gaussian processes and Hammerstein integral equations
    • M. Pincus, Gaussian processes and Hammerstein integral equations, Trans. Amer. Math. Soc. 134 (1968) 193-216.
    • (1968) Trans. Amer. Math. Soc. , vol.134 , pp. 193-216
    • Pincus, M.1
  • 42
    • 77956140700 scopus 로고
    • The Laplace method for probability measures in Banach spaces
    • V. I. Piterbarg and V. R. Fatalov, The Laplace method for probability measures in Banach spaces, Russian Math. Surveys 50 (1995) 1151-1239.
    • (1995) Russian Math. Surveys , vol.50 , pp. 1151-1239
    • Piterbarg, V.I.1    Fatalov, V.R.2
  • 43
    • 0011306083 scopus 로고
    • The method of stationary phase for oscillatory integrals on Hubert spaces
    • J. Rezende, The method of stationary phase for oscillatory integrals on Hubert spaces, Comm. Math. Phys. 101 (1985) 187-206.
    • (1985) Comm. Math. Phys. , vol.101 , pp. 187-206
    • Rezende, J.1
  • 45
    • 84968484534 scopus 로고
    • Some asymptotic formulas for Wiener integrals
    • M. Schilder, Some asymptotic formulas for Wiener integrals, Trans. Amer. Math. Soc. 125 (1966) 63-85.
    • (1966) Trans. Amer. Math. Soc. , vol.125 , pp. 63-85
    • Schilder, M.1
  • 47
    • 0001021846 scopus 로고    scopus 로고
    • Oscillatory integrals with quadratic phase function on a real abstract Wiener space
    • H. Sugita and S. Taniguchi, Oscillatory integrals with quadratic phase function on a real abstract Wiener space, J. Fund. Anal. 152 (1998).
    • (1998) J. Fund. Anal. , vol.152
    • Sugita, H.1    Taniguchi, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.