Stochastic Calculus and Stochastic Filtering

Stochastic Calculus and Stochastic Filtering

Provides a very informal introduction to Stochastic Calculus, and especially to the Ito integral and some of its applications.

Publication date: 10 Apr 2006

ISBN-10: n/a

ISBN-13: n/a

Paperback: n/a

Views: 14,406

Type: N/A

Publisher: n/a

License: n/a

Post time: 02 Jan 2007 08:08:20

Stochastic Calculus and Stochastic Filtering

Stochastic Calculus and Stochastic Filtering Provides a very informal introduction to Stochastic Calculus, and especially to the Ito integral and some of its applications.
Tag(s): Operations Research
Publication date: 10 Apr 2006
ISBN-10: n/a
ISBN-13: n/a
Paperback: n/a
Views: 14,406
Document Type: N/A
Publisher: n/a
License: n/a
Post time: 02 Jan 2007 08:08:20
Notes Excerpts:

The following notes aim to provide a very informal introduction to Stochastic Calculus, and especially to the Ito integral and some of its applications. They owe a great deal to Dan Crisan's Stochastic Calculus and Applications lectures of 1998; and also much to various books especially those of L. C. G. Rogers and D. Williams, and Dellacherie and Meyer's multi volume series 'Probabilities et Potentiel'. They have also benefited from insights gained by attending lectures given by T. Kurtz.

The goal of the notes in their current form is to present a fairly clear approach to the Ito integral with respect to continuous semimartingales but without any attempt at maximal detail. The various alternative approaches to this subject which can be found in books tend to divide into those presenting the integral directed entirely at Brownian Motion, and those who wish to prove results in complete generality for a semimartingale. Here at all points clarity has hopefully been the main goal here, rather than completeness; although secretly the approach aims to be readily extended to the discontinuous theory. The notes contain proofs which spell out every minute detail, since on a first look at the subject the purpose of some of the steps in a proof often seems elusive. The notes intent to show the reader that the Ito integral isn't that much harder in concept than the Lebesgue Integral with which we are all familiar. The motivating principle is to try and explain every detail, no matter how trivial it may seem once the subject has been understood.




About The Author(s)


No information is available for this author.

Alan Bain

No information is available for this author.


Book Categories
Sponsors
Icons8, a free icon pack