Stochastic Integration in Abstract Spaces
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We establish the existence of a stochastic integral in a nuclear space setting as follows. Let , , and be nuclear spaces which satisfy the following conditions: the spaces are reflexive, complete, bornological spaces such that their strong duals also satisfy these conditions. Assume that there is a continuous bilinear mapping of into . If is an integrable, -valued predictable process and is an -valued square integrable martingale, then there exists a -valued process called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.
1986 ◽
Vol 41
(3)
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pp. 229-230
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1973 ◽
Vol 16
(2)
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pp. 269-273
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2015 ◽
Vol 22
(4)
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pp. 550-552
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1966 ◽
Vol 17
(1)
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pp. 148-148
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1986 ◽
Vol 100
(1)
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pp. 151-159
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