Elements of Stochastic Calculus and Analysis by Daniel W. Stroock

Author:Daniel W. Stroock
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

where with .

The following corollary is an observation made by Itô after he cleaned up Wiener’s treatment of (3.5.5). It is often called Itô’s representation theorem and turns out to play an important role in applications of stochastic analysis to, of all things, models of financial markets.9

Corollary 3.5.4.

The map

is a linear, isometric surjection. Hence, for each there is a -almost surely unique such that

In particular,

Finally, for any , there is a version of that is continuous as function of .

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