Stochastic Integration and Differential Equations / Edition 2

Stochastic Integration and Differential Equations / Edition 2

by Philip Protter
ISBN-10:
3642055605
ISBN-13:
9783642055607
Pub. Date:
12/01/2010
Publisher:
Springer Berlin Heidelberg
ISBN-10:
3642055605
ISBN-13:
9783642055607
Pub. Date:
12/01/2010
Publisher:
Springer Berlin Heidelberg
Stochastic Integration and Differential Equations / Edition 2

Stochastic Integration and Differential Equations / Edition 2

by Philip Protter
$129.99
Current price is , Original price is $129.99. You
$129.99 
  • SHIP THIS ITEM
    In stock. Ships in 1-2 days.
  • PICK UP IN STORE

    Your local store may have stock of this item.


Overview

It has been 15 years since the first edition of Shastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and shastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach".

The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space Hsub1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.


Product Details

ISBN-13: 9783642055607
Publisher: Springer Berlin Heidelberg
Publication date: 12/01/2010
Series: Stochastic Modelling and Applied Probability , #21
Edition description: Second Edition 2005
Pages: 415
Product dimensions: 6.10(w) x 9.20(h) x 0.70(d)

Table of Contents

I Preliminaries.- II Semimartingales and Shastic Integrals.- III Semimartingales and Decomposable Processes.- IV General Shastic Integration and Local Times.- V Shastic Differential Equations.- VI Expansion of Filtrations.- References.
From the B&N Reads Blog

Customer Reviews