Stochastic Processes for Physicists: Understanding Noisy SystemsCambridge University Press, 18 de fev. de 2010 - 204 páginas Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is included, as is a concise account of numerical methods for simulating stochastic systems driven by Gaussian noise. The book concludes with a non-technical introduction to the concepts and jargon of measure-theoretic probability theory. With over 70 exercises, this textbook is an easily accessible introduction to stochastic processes and their applications, as well as methods for numerical simulation, for graduate students and researchers in physics. |
Conteúdo
| 1 | |
2 Differential equations | 16 |
3 Stochastic equations with Gaussian noise | 26 |
4 Further properties of stochastic processes | 55 |
5 Some applications of Gaussian noise | 71 |
6 Numerical methods for Gaussian noise | 91 |
7 FokkerPlanck equations and reactiondiffusion systems | 102 |
8 Jump processes | 127 |
9 Levy processes | 151 |
10 Modern probability theory | 166 |
Calculating Gaussian integrals | 181 |
References | 184 |
| 186 | |
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Stochastic Processes for Physicists: Understanding Noisy Systems Kurt Jacobs Prévia não disponível - 2010 |
Termos e frases comuns
8-function a-stable approximation asset auto-correlation function average AW)² Brownian motion called Cauchy Chapter characteristic function conditional probability consider constant correlation defined denote derivative described deterministic dW)² exit expectation value exponential finite Fokker-Planck equation forward contract Fourier transform FP equation Gaussian noise Gaussian random variables given independent infinite initial condition interval Ito calculus Ito integral joint probability density jump process jump rate Levy processes linear stochastic equation master equation matrix mean and variance measure molecule multiply neuron noise sources Note o-algebra obtain option particle Pin(t Poisson process portfolio probability density probability theory random increments result sample path sample space Section signal simple simulation solution solve stationary steady-state stochastic differential equations stochastic integral stochastic process Stratonovich integral t)dt t)dW time-step vector Wiener increment Wiener noise Wiener process write zero дх