A translation of an analogue of Wiener space with its applications on their product spaces
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Let $C[0,T]$ denote an analogue of Weiner space, the space of real-valued continuous on $[0,T]$. In this paper, we investigate the translation of time interval $[0,T]$ defining the analogue of Winer space $C[0,T]$. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on $C[0,T]$ as the analogue of Wiener measures on $C[0,s]$ and $C[s,T]$ with $0<s<T$.
Abstract
Let $C[0,T]$ denote an analogue of Weiner space, the space of real-valued continuous on $[0,T]$. In this paper, we investigate the translation of time interval $[0,T]$ defining the analogue of Winer space $C[0,T]$. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on $C[0,T]$ as the analogue of Wiener measures on $C[0,s]$ and $C[s,T]$ with $0<s<T$.
참고문헌 (12)
- R. H. Cameron, "Transformations of Weiner Integrals Under Translations", The Annals of Mathematics, 45(2), pp.386~396 (1944), JSTOR[DOI]
- ), "Journal of Fourier Analysis and Applications", 2009, 441~462, pp.Springer Science and Business Media LLC, https:
- R. A. Ewan, "The Cameron-Storvick operator-valued function space integrals for a class of nite-dimensional functionals", Ph.D, pp.1973
- T. Hida, "Brownian motion" (1980), Springer-Verlag
- 임만규, "An analogue of Wiener measure and its applications", 대한수학회지, 39(5), pp.801~819 (2002), 대한수학회
- H. H. Kuo, "Gaussian measures in Banach spaces" (1975), Springer-Verlag
- 류근식, "THE GENERALIZED ANALOGUE OF WIENER MEASURE SPACE AND ITS PROPERTIES", 호남수학학술지, 32(4), pp.633~642 (2010), 호남수학회
- 류근식, "The translation theorem on the generalized analogue of Wiener space and its applications", 충청수학회지, 26(4), pp.735~742 (2013), 충청수학회[DOI]
- K. S. Ryu, "A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula", Transactions of the American Mathematical Society, 354(12), pp.4921~4951 (2002), American Mathematical Society (AMS)[DOI]
- K. Ryu, "On a measure in Wiener space and applications", Transactions of the American Mathematical Society, 355(6), pp.2205~2222 (2003), American Mathematical Society (AMS)[DOI]
- N. Wiener, "Dierential-space", J. Math. and Phys, 2, pp.131~174 (1923)
- J. Yeh, "Stochastic processes and the Wiener integral" (1973), Marcel Dekker, Inc