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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Probability and Stochastic Processes for Physicists (Paperback, 1st ed. 2020)
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Probability and Stochastic Processes for Physicists (Paperback, 1st ed. 2020)
Series: UNITEXT for Physics
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This book seeks to bridge the gap between the parlance, the models,
and even the notations used by physicists and those used by
mathematicians when it comes to the topic of probability and
stochastic processes. The opening four chapters elucidate the basic
concepts of probability, including probability spaces and measures,
random variables, and limit theorems. Here, the focus is mainly on
models and ideas rather than the mathematical tools. The discussion
of limit theorems serves as a gateway to extensive coverage of the
theory of stochastic processes, including, for example,
stationarity and ergodicity, Poisson and Wiener processes and their
trajectories, other Markov processes, jump-diffusion processes,
stochastic calculus, and stochastic differential equations. All
these conceptual tools then converge in a dynamical theory of
Brownian motion that compares the Einstein-Smoluchowski and
Ornstein-Uhlenbeck approaches, highlighting the most important
ideas that finally led to a connection between the Schroedinger
equation and diffusion processes along the lines of Nelson's
stochastic mechanics. A series of appendices cover particular
details and calculations, and offer concise treatments of
particular thought-provoking topics.
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