From Tanaka’s Formula to Ito’s Formula: Distributions, Tensor Products and Local Times View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2001

AUTHORS

B. Rajeev

ABSTRACT

In this article we study the classical finite dimensional Ito formula from an infinite dimensional perspective. A finite dimensional semi-martingale is represented as a semi-martingale in a (countable) Hilbert space of tempered distributions. The classical Ito formula is obtained on action by a test function from the dual space. Finite dimensional stochastic differential equations with smooth coefficients are represented as an SDE in a Hilbert space. We obtain representations of the local time process, viewed as a distribution in the space varible, in terms of a Hilbert space valued process of finite variation. A basic feature of our representation, is the role of the tensor product. More... »

PAGES

371-389

Book

TITLE

Séminaire de Probabilités XXXV

ISBN

978-3-540-41659-3
978-3-540-44671-2

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-44671-2_25

DOI

http://dx.doi.org/10.1007/978-3-540-44671-2_25

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1013068276


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