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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On infinite dimensional Ito's formula


Author: T. F. Lin
Journal: Proc. Amer. Math. Soc. 49 (1975), 219-226
MSC: Primary 60H05; Secondary 60J60
MathSciNet review: 0380984
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Abstract: Ito's formula for $ Y(t)g(t,\xi (t))$ is given where $ g$ is a Hilbert space valued function, $ \xi (t)$ is a diffusion on Hilbert space and $ Y(t)$ is an operator-valued stochastic integral w.r.t. $ \xi (t)$. A stochastic integral representation for solution of a certain second order parabolic equation is also given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0380984-6
PII: S 0002-9939(1975)0380984-6
Keywords: $ S$-operator, trace, stochastic integral, Ito's formula, parabolic equation
Article copyright: © Copyright 1975 American Mathematical Society