Stochastic Integrals in Abstruct Wiener Space II: Regularity Properties

作者: Hui-Hsiung Kuo

DOI: 10.1017/S0027763000015592

关键词: Abstract Wiener spaceReflection principle (Wiener process)Paley–Wiener integralReflected Brownian motionMathematical analysisIntegral representation theorem for classical Wiener spacePure mathematicsBessel processStochastic differential equationMathematicsClassical Wiener space

摘要: This paper continues the study of stochastic integrals in 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 Wiener space.

参考文章(18)
Leonard Gross, Abstract Wiener spaces Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Contributions to Probability Theory, Part 1. pp. 31- 42 ,(1967)
Kiyosi Itô, On a Formula Concerning Stochastic Differentials Nagoya Mathematical Journal. ,vol. 3, pp. 55- 65 ,(1951) , 10.1017/S0027763000012216
Kiyosi Itô, Makiko Nisio, On the convergence of sums of independent Banach space valued random variables Osaka Journal of Mathematics. ,vol. 5, pp. 35- 48 ,(1968) , 10.18910/11410
Hiroshi Kunita, Stochastic Integrals Based on Martingales Taking Values in Hilbert Space Nagoya Mathematical Journal. ,vol. 38, pp. 41- 52 ,(1970) , 10.1017/S0027763000013507
Hiroshi Kunita, Shinzo Watanabe, On Square Integrable Martingales Nagoya Mathematical Journal. ,vol. 30, pp. 209- 245 ,(1967) , 10.1017/S0027763000012484
Leonard Gross, MEASURABLE FUNCTIONS ON HILBERT SPACE Transactions of the American Mathematical Society. ,vol. 105, pp. 372- 390 ,(1962) , 10.1090/S0002-9947-1962-0147606-6
M. Ann Piech, A fundamental solution of the parabolic equation on Hilbert space. II. The semigroup property Transactions of the American Mathematical Society. ,vol. 150, pp. 257- 286 ,(1970) , 10.1090/S0002-9947-1970-0278116-8
Hui Hsiung Kuo, Diffusion and Brownian motion on infinite-dimensional manifolds Transactions of the American Mathematical Society. ,vol. 169, pp. 439- 459 ,(1972) , 10.1090/S0002-9947-1972-0309206-0
M. Ann Piech, Diffusion semigroups on abstract Wiener space Transactions of the American Mathematical Society. ,vol. 166, pp. 411- 430 ,(1972) , 10.1090/S0002-9947-1972-0295141-3
M.Ann Piech, Some regularity properties of diffusion processes on abstract Wiener space Journal of Functional Analysis. ,vol. 8, pp. 153- 172 ,(1971) , 10.1016/0022-1236(71)90024-3