Kasahara, Yuji; Watanabe, Shinzo Remarks on Krein-Kotani’s correspondence between strings and Herglotz functions. (English) Zbl 1177.47053 Proc. Japan Acad., Ser. A 85, No. 3, 22-26 (2009). Reviewer: Bilender P. Allahverdiev (Isparta) MSC: 47E05 34L05 60J55 60G51 PDFBibTeX XMLCite \textit{Y. Kasahara} and \textit{S. Watanabe}, Proc. Japan Acad., Ser. A 85, No. 3, 22--26 (2009; Zbl 1177.47053) Full Text: DOI
Kasahara, Yuji; Watanabe, Shinzo Occupation time theorems for one-dimensional random walks and diffusion processes in random environments. (English) Zbl 1161.60025 Stochastic Processes Appl. 119, No. 2, 347-372 (2009). Reviewer: Elisaveta Pancheva (Sofia) MSC: 60J55 60J60 60G51 60G52 PDFBibTeX XMLCite \textit{Y. Kasahara} and \textit{S. Watanabe}, Stochastic Processes Appl. 119, No. 2, 347--372 (2009; Zbl 1161.60025) Full Text: DOI Link
Kasahara, Yuji; Watanabe, Shinzo Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes. (English) Zbl 1102.60066 Ill. J. Math. 50, No. 1-4, 515-539 (2006). Reviewer: Victoria Knopova (Kiev) MSC: 60J55 60J60 60G51 60G52 PDFBibTeX XMLCite \textit{Y. Kasahara} and \textit{S. Watanabe}, Ill. J. Math. 50, No. 1--4, 515--539 (2006; Zbl 1102.60066)
Kasahara, Yuji; Watanabe, Shinzo Occupation time theorems for a class of one-dimensional diffusion processes. (English) Zbl 1098.60080 Period. Math. Hung. 50, No. 1-2, 175-188 (2005). Reviewer: Heinrich Hering (Rockenberg) MSC: 60J60 60J55 PDFBibTeX XMLCite \textit{Y. Kasahara} and \textit{S. Watanabe}, Period. Math. Hung. 50, No. 1--2, 175--188 (2005; Zbl 1098.60080) Full Text: DOI
Watanabe, Shinzo Stochastic analysis on Wiener space. (English) Zbl 0899.60042 Mendrekar, V. (ed.) et al., Proceedings of the Norbert Wiener centenary congress, East Lansing, MI, USA, November 27–December 3, 1994. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 52, 359-370 (1997). MSC: 60G44 60H07 60H10 PDFBibTeX XMLCite \textit{S. Watanabe}, Proc. Symp. Appl. Math. 52, 359--370 (1997; Zbl 0899.60042)
Watanabe, Shinzo Generalized arc-sine laws for one-dimensional diffusion processes and random walks. (English) Zbl 0824.60080 Cranston, Michael C. (ed.) et al., Stochastic analysis. Proceedings of the Summer Research Institute on stochastic analysis, held at Cornell University, Ithaca, NY, USA, July 11-30, 1993. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 57, 157-172 (1995). Reviewer: J.Bertoin (Paris) MSC: 60J60 60J55 PDFBibTeX XMLCite \textit{S. Watanabe}, Proc. Symp. Pure Math. 57, 157--172 (1995; Zbl 0824.60080)
Watanabe, Shinzo Fractional order Sobolev spaces on Wiener space. (English) Zbl 0792.60049 Probab. Theory Relat. Fields 95, No. 2, 175-198 (1993). Reviewer: S.Watanabe (Kyoto) MSC: 60H07 60H10 PDFBibTeX XMLCite \textit{S. Watanabe}, Probab. Theory Relat. Fields 95, No. 2, 175--198 (1993; Zbl 0792.60049) Full Text: DOI
Takanobu, S.; Watanabe, S. Asymptotic expansion formulas of the Schilder type for a class of conditional Wiener functional integrations. (English) Zbl 0801.60020 Elworthy, K. D. (ed.) et al., Asymptotic problems in probability theory: Wiener functionals and asymptotics. Proceedings of the 26th Taniguchi international symposium, Sanda and Kyoto, Japan, August 31 - September 5, 1990. Harlow, Essex: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 284, 194-241 (1993). Reviewer: W.Bryc (Cincinnati) MSC: 60F10 60H07 PDFBibTeX XMLCite \textit{S. Takanobu} and \textit{S. Watanabe}, Pitman Res. Notes Math. Ser. 284, 194--241 (1993; Zbl 0801.60020)
Watanabe, Shinzo A fractional calculus on Wiener space. (English) Zbl 0783.60065 Cambanis, Stamatis (ed.) et al., Stochastic processes: a festschrift in honour of Gopinath Kallianpur. New York: Springer-Verlag. 341-348 (1993). MSC: 60H99 60G20 PDFBibTeX XMLCite \textit{S. Watanabe}, in: Stochastic processes: a Festschrift in honour of Gopinath Kallianpur. New York: Springer-Verlag. 341--348 (1993; Zbl 0783.60065)
Watanabe, Shinzo Some refinement of conditional expectations on Wiener space by means of Malliavin calculus. (English) Zbl 0817.60064 Shiryaev, A. N. (ed.) et al., Probability theory and mathematical statistics. Proceedings of the 6th USSR-Japan symposium, Kiev, USSR, 5-10 August, 1991. Singapore: World Scientific. 414-421 (1992). MSC: 60H07 PDFBibTeX XMLCite \textit{S. Watanabe}, in: Probability theory and mathematical statistics. Proceedings of the 6th USSR-Japan symposium, Kiev, USSR, 5-10 August, 1991. Singapore: World Scientific. 414--421 (1992; Zbl 0817.60064)
Watanabe, Shinzo Short time asymptotic problems in Wiener functional integration theory. Applications to heat kernels and index theorems. (English) Zbl 0723.60060 Stochastic analysis and related topics II, Proc. 2nd Workshop, Silivri/Turk. 1988, Lect. Notes Math. 1444, 1-62 (1990). Reviewer: R.W.R.Darling (Tampa) MSC: 60H07 58J20 58J65 PDFBibTeX XML
Uemura, Hideaki; Watanabe, Shinzo Diffusion processes and heat kernels on certain nilpotent groups. (English) Zbl 0658.60109 Stochastic analysis, Proc. Jap.-Fr. Semin., Paris/France 1987, Lect. Notes Math. 1322, 173-197 (1988). Reviewer: H.Uemura MSC: 60J60 PDFBibTeX XML
Watanabe, Shinzo Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. (English) Zbl 0633.60077 Ann. Probab. 15, 1-39 (1987). Reviewer: S.Kusuoka MSC: 60H07 60H10 28C20 35K05 58J65 PDFBibTeX XMLCite \textit{S. Watanabe}, Ann. Probab. 15, 1--39 (1987; Zbl 0633.60077) Full Text: DOI
Ikeda, N.; Watanabe, S. Malliavin calculus of Wiener functionals and its applications. (English) Zbl 0612.60049 From local times to global geometry, control and physics, Emanations from Warwick Symp. Stochastic diff. equations appl., Coventry/Engl. 1984/85, Pitman Res. Notes Math. Ser. 150, 132-178 (1986). Reviewer: A.Yu.Veretennikov MSC: 60H10 60G30 58J35 PDFBibTeX XML
Ikeda, Nobuyuki; Watanabe, Shinzo Stochastic flows of diffeomorphisms. (English) Zbl 0561.60079 Stochastic analysis and applications, Adv. Probab. Relat. Top. 7, 179-198 (1984). Reviewer: Wilfrid S.Kendall MSC: 60J60 58J65 60H10 PDFBibTeX XML
Ikeda, Nobuyuki; Watanabe, Shinzo An introduction to Malliavin’s calculus. (English) Zbl 0546.60055 Stochastic analysis, Proc. Taniguchi Int. Symp., Katata & Kyoto/Jap. 1982, North-Holland Math. Libr. 32, 1-52 (1984). Reviewer: M.Breger MSC: 60Hxx 60H10 60J60 PDFBibTeX XML
Watanabe, S. Lectures on stochastic differential equations and Malliavin calculus. (English) Zbl 0546.60054 Lectures on Mathematics and Physics. Mathematics, 73. Tata Institute of Fundamental Research. Berlin etc.: Springer-Verlag. V, 118 p. DM 20.00; $ 7.30 (1984). Reviewer: M.Breger MSC: 60Hxx 60H10 60-02 60J60 PDFBibTeX XML
Watanabe, S. A limit theorem for sums of i.i.d. random variables with slowly varying tail probability. (English) Zbl 0434.60006 Multivariate analysis V, Proc. 5th int. Symp., Pittsburgh 1978, 249-261 (1980). MSC: 60B10 60G50 60J55 60J65 PDFBibTeX XML
Watanabe, Shinzo Poisson point process of Brownian excursions and its applications to diffusion processes. (English) Zbl 0391.60071 Probab., Proc. Symp. Pure Math., Urbana 1976, 153-164 (1977). MSC: 60J65 60J60 60J55 60H05 PDFBibTeX XML