Random Processes in Physics and Finance
Random Processes in Physics and Finance
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Abstract
This book discusses random processes in physics, from basic probability theory to the Fokker-Planck process and Langevin equation for the Fokker Planck process and diffusion. It 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. The name ‘econophysics’ has been used to denote the use of the mathematical techniques developed for the study of random processes in physical systems to applications in the economic and financial worlds. Since a substantial number of physicists are now employed in the financial arena or are doing research in this area, it is appropriate to give a course that emphasises and relates physical applications to financial applications. The course and text in this book differ from mathematical texts by emphasising the origins of noise, as opposed to an analysis of its transformation by linear and nonlinear devices. Among other topics, this book discusses thermal noise, shot noise, fluctuation-dissipation theorem, and delta functions.
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Front Matter
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1
Review of probability
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2
What is a random process
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3
Examples of Markovian processes
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4
Spectral measurement and correlation
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5
Thermal noise
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6
Shot noise
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7
The fluctuation–dissipation theorem
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8
Generalized Fokker–Planck equation
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9
Langevin processes
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10
Langevin treatment of the Fokker–Planck process
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11
The rotating wave van del Pol oscillator (RWVP)
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12
Noise in homogeneous semiconductors
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13
Random walk of light in turbid media
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14
Analytical solution of the elastic transport equation
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15
Signal extraction in presence of smoothing and noise
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16
Stochastic methods in investment decision
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17
Spectral analysis of economic time series
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End Matter
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