Stochastic integral representation of some martingales
نویسندگان
چکیده
منابع مشابه
Functional Ito calculus and stochastic integral representation of martingales
We develop a non-anticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by B Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative ad...
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Let (fn) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (dn) from [0, 1] such that ∫ 1 0 dn(x1, . . . , xn)dxn = 0 for almost all x1, . . . , xn−1, and such that the law of (fn) is the same as the law of ( ∑n k=1 dk(x1, . . . , xk)). Similar results for tangent sequences and sequences satisfying condition (C.I.) are presented. We also present a weaker...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1977
ISSN: 0022-247X
DOI: 10.1016/0022-247x(77)90197-4