Random Processes in Physics and Finance

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Overview

This respected high-level text is aimed at students and professionals working on random processes in various areas, including physics and finance. The first author, Melvin Lax (1922-2002) was a distinguished Professor of Physics at City College of New York and a member of the U. S. National Academy of Sciences, and is widely known for his contributions to our understanding of random processes in physics. Most chapters of this book are outcomes of the class notes which Lax taught at the City University of New York from 1985 to 2001. The material is unique as it presents the theoretical framework of Lax's treatment of random processes, from basic probability theory to Fokker-Planck and Langevin Processes, and includes diverse applications, such as explanations of very narrow laser width, analytical solutions of the elastic Boltzmann transport equation, and a critical viewpoint of mathematics currently used in the world of finance.

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Editorial Reviews

From the Publisher
"One challenge in adequately preparing physics students to contribute to economics has been the absence of a comprehensive and rigorous monograph that presents the physical laws governing random processes...Random Processes in Physics and Finance, by the late Melvin Lax and completed by coauthors Wei Cai and Min Xu, rises admirably to the challenge."—Physics Today
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Product Details

  • ISBN-13: 9780198567769
  • Publisher: Oxford University Press
  • Publication date: 11/30/2006
  • Series: Oxford Finance Series
  • Pages: 342
  • Product dimensions: 9.50 (w) x 6.80 (h) x 0.90 (d)

Meet the Author

Melvin Lax (Deceased)
Distinguished Professor of Physics
City College of New York

Melvin Lax was a Distinguished Professor of Physics at the City College of the City University of New York (1971-2002), and a member of the U. S. National Academy of Sciences (1983-2002).
He has been associated with Bell Laboratories as a member of the technical staff (1955-1972), as head of the Theoretical Physics Research Department (1962-1964) and as consultant to the Solid State Electronics Research Laboratory.
After receiving his PhD in Physics from MIT (1947), Dr. Lax advanced from assistant to full professor of Physics at Syracuse University, (1947-55). He has also taught at Princeton (Spring 1961) and at Oxford (1961-1962). Dr. lax has published more than 200 papers.
In 1999 Lax shared the Willis Lamb Medal for Laser Science and Quantum Optics.
Dr. Lax was listed Who's Who in America.
Wei Cai
Senior research staff
Institute for Ultrafast Spectroscopy and lasers
Department of Physics
City College of New York

Wei Cai received Ph. D degree in Physics from University of Houston in 1985. He also received a MS degree in computer science from City College of City University of New York in 1992. He joined the Department of Physics at the City College of the City University of New York as a research associate in 1985. Recently, he is a senior member of the research staff at the Institute for Ultrafast Spectroscopy and Lasers. His main research interests are in radiative transfer and optical image processing. He has published 55 papers and holds 4 U. S. Patent.
Min Xu
Research staff
Institute for Ultrafast Spectroscopy and lasers
Department of Physics
City College of New York

Min Xu received Ph. D degree in Physics from City University of New York in 2001. He is currently a research associate at the Institute for Ultrafast Spectroscopy and Lasers. He works at the interface of physics, engineering and biomedical sciences. His main research interests are in optical physics, stochastic processes and inverse problems in physical and biological sciences, in particular, biomedical optical spectroscopy and imaging. He has published 30 peer-reviewed journal papers and holds 1 U. S. Patent.

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Table of Contents

1. Review of Probability
2. What is a Random Process
3. Examples of Markovian Processes
4. Spectral Measurement and Correlation
5. Thermal Noise
6. Shot Noise
7. The Fluctuation-Dissipation Theorem
8. Generalized Fokker-Planck Equation of Markov Process
9. Langevin Process
10. Langevin Treatment of the Fokker-Planck Process
11. The Rotating Wave Van Del Pol Oscillator (RWVP)
12. Noise in Homogeneous Semiconductors
13. Random Walk of Light in Turbid Media
14. Analytical Solution of the Elastic Boltzmann Transport Equation
15. Signal Extraction in the Presence of Smoothing and Noise
16. Stochastic Methods to Investment Decision
17. Spectral Analysis of Economic Time Series

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