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Stochastic Integrals in Abstruct Wiener Space II: Regularity Properties

Published online by Cambridge University Press:  22 January 2016

Hui-Hsiung Kuo
Hui-Hsiung Kuo*
Affiliation:
Department of Mathematics, University of Virginia Charlottesville, Va., U.S.A.
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This paper continues the study of stochastic integrals in abstract Wiener space previously given in [14]. We will present, among other things, the detailed discussion and proofs of the results announced in [16]. Let H ⊂ B be an abstract Wiener space.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 50 , June 1973, pp. 89 - 116
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Dalec’kii, Yu. L., Differential equations with functional derivatives and stochastic equations for generalized random processes (English translation), Soviet Math. Dokl., 7 (1966), 220–223.Google Scholar
[2] Dalec’kii, Yu. L., Infinite-dimensional elliptic operators and parabolic equations connected with them (English translation), Russian Math. Surveys, 22 (1967), 1–53.Google Scholar
[3] Gikhman, I.I., On the theory of differential equations of random processes (in Russian), Ukr. Matem. Zhurn., 2 (1950), 37–63.Google Scholar
[4] Gikhman, I.I., On the theory of differential equations of random processes II (in Russian), ibid. 3 (1951), 317–339.Google Scholar
[5] Gross, L., Abstract Wiener spaces, Proc. 5th Berkeley Sym. Math. Stat. Prob., 2 (1965), 31–42.Google Scholar
[6] Gross, L., Measurable functions on Hilbert space, Trans. Amer. Math. Soc, 105 (1962), 372–390.Google Scholar
[7] Gross, L., Potential theory on Hilbert space, J. Func. Anal. 1 (1967), 123–181.Google Scholar
[8] Ito, K., On a formula concerning stochastic differentials, Nagoya Math. J., 3 (1951), 55–65.CrossRefGoogle Scholar
[9] Ito, K. and Nisio, M., On the convergence of sums of independent Banach space valued random variables, Osaka J. Math., 5 (1968), 35–48.Google Scholar
[10] Kannan, D., An operator-valued stochastic integral II, Ann. Inst. Henri Poincaré, Section B, 8 (1972), 9–32.Google Scholar
[11] Kannan, D. and Bharucha-Reid, A. T., An operator-valued stochastic integral, Proc. Japan Acad., 47 (1971), 472–476.Google Scholar
[12] Kunita, H., Stochastic integrals based on martingales taking values in Hilbert space, Nagoya Math. J., 38 (1970), 41–52.Google Scholar
[13] Kunita, H. and Watanabe, S., On square integrable martingales, Nagoya Math. J., 30 (1967), 209–245.Google Scholar
[14] Kuo, H.-H., Stochastic integrals in abstract Wiener space, Pacific J. Math., 41 (1972), 469–483.Google Scholar
[15] Kuo, H.-H., Diffusion and Brownian motion on infinite dimensional manifolds, Trans. Amer. Math. Soc, 169 (1972), 439–459.Google Scholar
[16] Kuo, H.-H., On operator-valued stochastic integrals, Bulletin Amer. Math. Soc, 79 (1973), 207–210.CrossRefGoogle Scholar
[17] Kuo, H.-H., and Piech, M. A., Stochastic integrals and parabolic equations in abstract Wiener space, Bulletin Amer. Math. Soc. (to appear).Google Scholar
[18] McKean, H.P., Stochastic integrals, Academic Press, New York-London (1969).Google Scholar
[19] Piech, M.A., A fundamental solution of the parabolic equation on Hilbert space, J. Fune Anal., 3 (1969), 85–114.Google Scholar
[20] Piech, M.A., A fundamental solution of the parabolic equation on Hilbert space II: The semi-group property, Trans. Amer. Math. Soc, 150 (1970), 257–286.Google Scholar
[21] Piech, M.A., Some regularity property of diffusion processes on abstract Wiener space, J. Func Anal., 8 (1971), 153–172.CrossRefGoogle Scholar
[22] Piech, M.A., Diffusion semigroups on abstract Wiener space, Trans. Amer. Math. Soc, 166 (1972), 411–430.Google Scholar
[23] Skorokhod, A.V., Introduction to the theory of random processes (English translation), Saunders Company, Philadelphia-London-Toronto (1969).Google Scholar