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Revuz, D. and Yor, M., Continuous Martingales and Brownian Motion, Berlin: Springer, 1999, 3rd ed. Borodin, A.N. and Salminen, P., Handbook of Brownian Motion: Facts and Formulae, Basel: Birkhäuser, 1996. Translated under the title Spravochnik po brounovskomu dvizheniyu, St. Petersburg: Lan’, 2000. Bulinskii, A.V. and Shiryaev, A.N., Teoriya sluchainykh protsessov (Theory of Stochastic Processes), Moscow: Fizmatlit, 2003. Øksendal, B.K., Stochastic Differential Equations: An Introduction with Applications, Berlin: Springer, 2003, 6th ed. Translated under the title Stokhasticheskie differentsial’nye uravneniya, Moscow: Mir, 2003. Shiryaev, A.N., Osnovy stokhasticheskoi finansovoi matematiki, 2 vols., Moscow: FAZIS, 1998. Translated under the title Essentials of Stochastic Finance: Facts, Models, Theory, Singapore: World Scientific, 1999. Fatalov, V.R., Integral Functionals for the Exponent of a Wiener Process and Brownian Bridge: Exact Asymptotics and Legendre Functions, prepared for publication. Piterbarg, V.I. and Fatalov, V.R., Exact Asymptotics of Distributions of Integral Functionals for the Exponent of the Modulus of a Wiener Process and the MacDonald Function, prepared for publication. Piterbarg, V.I. and Fatalov, V.R., The Laplace Method for Probability Measures in Banach Spaces, Uspekhi Mat. Nauk, 1995, vol. 50, no. 6, pp. 57–150 [Russian Math. Surveys (Engl. Transl.), 1995, vol. 50, no. 6, pp. 1151–1239]. Fatalov, V.R., Exact Asymptotics of Large Deviations of Gaussian Measures in a Hilbert Space, Izv. Nats. Akad. Nauk Armenii Mat., 1992, vol. 27, no. 5, pp. 43–61 [J. Contemp. Math. Anal. (Engl. Transl.), 1992, vol. 27, no. 5, pp. 36–50]. Fatalov, V.R., Large Deviations of Gaussian Measures in the Spaces ℓp and L p, p ≥ 2, Teor. Veroyatnost. i Primenen., 1996, vol. 41, no. 3, pp. 682–689 [Theory Probab. Appl. (Engl. Transl.), 1996, vol. 41, no. 3, pp. 548–555]. Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Abramowitz, M. and Stegun, I.A., Eds., New York: Dover, 1965. Translated under the title Spravochnik po spetsial’nym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Moscow: Nauka, 1979. Bateman, H. and Erdélyi, A., Higher Transcendental Functions, New York: McGraw-Hill, 1953, vol. 1. Translated under the title Vysshie transtsendentnye funktsii, Moscow: Nauka, 1996, vol. 1. Robin, L., Fonctions sphériques de Legendre et fonctions sphéroïdales, 3 vols., Paris: Gauthier-Villars, 1957–1959. Hida, T., Brownian Motion, New York: Springer, 1980. Translated under the title Brounovskoe dvizhenie, Moscow: Nauka, 1987. Ikeda, N. and Watanabe, S., Stochastic Differential Equations and Diffusion Processes, Amsterdam: North-Holland; Tokyo: Kodansha, 1981. Translated under the title Stokhasticheskie differentsial’nye uravneniya i diffuzionnye protsessy, Moscow: Nauka, 1987. Luke, Y.L., The Special Functions and Their Approximations, New York: Academic, 1969. Translated under the title Spetsial’nye matematicheskie funktsii i ikh approksimatsii, Moscow: Mir, 1980. Lewin, L., Polylogarithms and Associated Functions, New York: North Holland, 1981. Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I., Integraly i ryady, vol. 1: Elementarnye funktsii (Elementary Functions), Moscow: Nauka, 1981. Translated under the title Integrals and Series, New York: Gordon & Breach, 1986. Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I., Integraly i ryady, vol. 3: Spetsial’nye funktsii. Dopolnitel’nye glavy (Special Functions. Advanced Chapters), Moscow: Nauka, 1986. Translated under the title Integrals and Series, New York: Gordon & Breach, 1986. Fatalov, V.R., Large Deviations of the L p-Norm of a Wiener Process with Drift, Mat. Zametki, 1999, vol. 65, no. 3, pp. 429–436 [Math. Notes (Engl. Transl.), 1999, vol. 65, no. 3–4, pp. 358–364]. Fatalov, V.R., Asymptotics of Large Deviations of Wiener Fields in the L p-Norm, Nonlinear Hammerstein Equations, and Higher-Order Hyperbolic Boundary Value Problems, Teor. Veroyatnost. i Primenen., 2002, vol. 47, no. 4, pp. 710–726 [Theory Probab. Appl. (Engl. Transl.), 2003, vol. 47, no. 4, pp. 623–636]. Fatalov, V.R., Asymptotics of Large Deviations of Gaussian Processes of Wiener Type for L p-Functionals, p > 0, and the Hypergeometric Function, Mat. Sb., 2003, vol. 194, no. 3, pp. 61–82 [Sb. Math. (Engl. Transl.), 2003, vol. 194, no. 3–4, pp. 369–390]. Fatalov, V. R. Exact Asymptotics of Large Deviations of Stationary Ornstein-Uhlenbeck Processes for L p-Functionals, p > 0, Probl. Peredachi Inf., 2006, vol. 42, no. 1, pp. 52–71 [Probl. Inf. Trans. (Engl. Transl.), 2006, vol. 42, no. 1, pp. 46–63]. Fatalov, V.R., Large Deviations for Gaussian Processes in the Hölder Norm, Izv. Ross. Akad. Nauk, Ser. Mat., 2003, vol. 67, no. 5, pp. 207–224 [Izv. Math. (Engl. Transl.), 2003, vol. 67, no. 5, pp. 1061–1079]. Piterbarg, V.I., Asimptoticheskie metody v teorii gaussovskikh protsessov i polei (Asymptotic Methods in the Theory of Gaussian Processes and Fields), Moscow: Izd. Mosk. Gos. Univ., 1988. Gikhman, I.I. and Skorokhod, A.V., Teoriya sluchainykh protsessov, vol. 1, Moscow: Nauka, 1971. Translated under the title The Theory of Stochastic Processes, vol. 1, Berlin: Springer, 1974. Kuo, H.-H., Gaussian Measures in Banach Spaces, Berlin: Springer, 1975. Translated under the title Gaussovskie mery v banakhovykh prostranstvakh, Moscow: Mir, 1979. Vakhaniya, N.N., Tarieladze, V.I., and Chobanyan, S.A., Veroyatnostnye raspredeleniya v banakhovykh prostrnstvakh, Moscow: Nauka, 1985. Translated under the title Probability Distributions on Banach Spaces, Dordrecht: Kluwer, 1987. Lifshits, M.A., Gaussovskie sluchainye funktsii, Kiev: TViMS, 1995. Translated under the title Gaussian Random Functions, Dordrecht: Kluwer, 1995. Bogachev, V.I., Gaussovskie mery, Moscow: Nauka/Fizmatlit, 1997. Translated under the title Gaussian Measures, Providence: AMS, 1998. Vainberg, M.M., Variatsionnyi metod i metod monotonnykh operatorov v teorii nelineinykh uravnenii, Moscow: Nauka, 1972. Translated under the title Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations, New York: Wiley, 1973. Alekseev, V.M., Tikhomirov, V.M., and Fomin, S.V. Optimal’noe upravlenie, Moscow: Nauka, 1979. Translated under the title Optimal Control, New York: Consultants Bureau, 1987. Bonic, R. and Frampton, J., Smooth Functions on Banach Manifolds, J. Math. Mech., 1966, vol. 15, no. 5, pp. 877–898. Kantorovich, L.V. and Akilov, G.P., Funktsional’nyi analiz, Moscow: Nauka, 1977, 2nd ed. Translated under the title Functional Analysis, Oxford: Pergamon, 1982. Simon, B., Functional Integration and Quantum Physics, New York: Academic, 1979. Funktsional’nyi analiz, Krein, S.G., Ed., Moscow: Nauka, 1972. Translated under the title Functional Analysis, Groningen: Wolters-Noordhoff, 1972. Pietsch, A., Operator Ideals, Amsterdam: North-Holland, 1980. Translated under the title Operatornye idealy, Moscow: Mir, 1982. Gokhberg, I.Ts. and Krein, M.G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gil’bertovom prostranstve, Moscow: Nauka, 1965. Translated under the title Introduction to the Theory of Linear Nonselfadjoint Operators, Providence: AMS, 1969. Prössdorf, S., Linear Integral Equations, in Itogi Nauki Tekh. Ser. Sovr. Probl. Mat. Fundam. Napravleniya, vol. 27, Moscow: VINITI, 1988, pp. 6–127. Akhiezer, N.I. and Glazman, I.M., Teoriya lineinykh operatorov v gil’bertovom prostranstve, Khar’kov: Vyshcha Shkola, 1977, 3rd ed. Translated under the title Theory of Linear Operators in Hilbert Space, Boston: Pitman, 1981. Fatalov, V.R., The Laplace Method for Computing Exact Asymptotics of Distributions of Integral Statistics, Math. Methods Statist., 1999, vol. 8, no. 4, pp. 510–535. Ellis, R.S. and Rosen, J.S., Laplace’s Method for Gaussian Integrals with an Application to Statistical Mechanics, Ann. Probab., 1982, vol. 10, no. 1, pp. 47–66; 1983, vol. 11, no. 2, p. 456. Krasnosel’skii, M.A. et al., Integral’nye operatory v prostranstvakh summiruemykh funktsii, Moscow: Nauka, 1966. Translated under the title Integral Operators in Spaces of Summable Functions, Leyden: Noordhoff, 1976. Riesz, F. and Szőkefalvi-Nagy, B., Leçons d’analyse fonctionnelle, Paris: Gauthier-Villars, 1965, 4th ed. Translated under the title Lektsii po funktsional’nomu analizu, Moscow: Mir, 1979. Sadovnichii, V.A., Teoriya operatorov, Moscow: Izd. Mosk. Gos. Univ., 1979. Translated under the title Theory of Operators, New York: Consultants Bureau, 1991. Kamke, E., Gewöhnliche Differentialgleichungen, vol. 1 of Differentialgleichungen; Lösungsmethoden und Lösungen, Leipzig: Geest & Portig, 1959, 6th ed. Translated under the title Spravochnik po obyknovennym differentsial’nym uravneniyam, Moscow: Nauka, 1971, 4th ed. Kostyuchenko, A.G. and Sargsyan, I.S., Raspredelenie sobstvennykh znachenii (samosopryazhennye obyknovennye differentsial’nye operatory) (Distribution of Eigenvalues: Self-adjoint Ordinary Differential Operators), Moscow: Nauka, 1979. Collatz, L., Eigenwertaufgaben mit technischen Anwendungen, Leipzig: Geest & Portig, 1963, 2nd ed. Translated under the title Zadachi na sobstvennye znacheniya s tekhnicheskimi prilozheniyami, Moscow: Nauka, 1968. Olver, F.W.J., Asymptotics and Special Functions, New York: Academic, 1974. Translated under the title Asimptotiki i spetsial’nye funktsii, Moscow: Nauka, 1990.