Philip Protter, Statistics Department, Columbia University

    Philip Protter

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2012 Discretization of Processes, Springer-Verlag, Heidelberg.

In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data.This book (written with Jean Jacod) establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. We present these latest techniques, based on research from the last 10 years. Some results appear in the book for the first time.



2005 Stochastic Integration and Differential Equations, Second Edition, Version 2.1 Springer-Verlag, Heidelberg.

This book treats stochastic calculus and differential equations in some generality, while nevertheless keeping the treatment relatively elementary and accessible. By using the Bichteler-Dellacherie theorem as the basis for an approach, a rapid introduction to the subject is given. Many of the usual theorems, such as Stricker's theorem, or that a semimartingale remains a semimartingale under a change to an equivalent probability measure, are transparently simple in this context.

The second edition has several significant changes, most prominently the addition of exercises for solution. Chapter 3 has been redone, with a new and more intuitive proof of the Doob-Meyer decomposition theorem, the more general version of Girsanov's theorem due to Lenglart, the Kazamaki-Novikov criteria for expoenetial local martingales to be martingales, and a modern treatment of compensators. Chapter 4 now treats sigma martingales and gives a more comprehensive treatment of martingale representation, including the Jacod-Yor theorem. A new chapter, Chapter 6, is an introduction to the theory of the expansion of filtrations.

A new "corrected third printing"' was released in April 2005. This is essentially a new version of the second edition, with more exercises, mistakes corrected, references updated, etc.; hence it is named Version 2.1.

Solutions to selected exercises for Chapters 1,2, and 3 are now available. The solutions have been graciously provided by Kazuhiro Shimbo.



2004 Probability Essentials, Second Edition Corrected Springer-Verlag, Heidelberg.

This book is intended to serve as the basis for a streamlined one semester course on measure theory based Probability Theory. It assumes no prior knowledge, and it is written with an applied audience in mind, such as Statisticians, Economists, or Engineers. Yet it is mathematically rigorous. It is designed so that one could use it for self study as well.

Solutions to selected exercises are now available. The solutions have been graciously provided by Deniz Sezer.



2003 L'essentiel en théorie des probabilités Cassini, Paris.

This book is the French version of Probability Essentials, Second Edition.



2003 1987 Calculus, Fourth Edition Jones & Bartlett, Boston

This text is a revision of the original text of Charles Morrey, Jr. and Murray Protter, Calculus and Analytic Geometry, Third Edition. It is modernized, while retaining the easy to read and yet thorough and correct style of the original.