Probability and Stochastic Processes for Physicists

1. Front Matter

   Pages i-xiii

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2. Probability

   1. Front Matter

      Pages 1-1

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   2. Probability Spaces

      • Nicola Cufaro Petroni

      Pages 3-18

   3. Distributions

      • Nicola Cufaro Petroni

      Pages 19-48

   4. Random Variables

      • Nicola Cufaro Petroni

      Pages 49-98

   5. Limit Theorems

      • Nicola Cufaro Petroni

      Pages 99-126

3. Stochastic Processes

   1. Front Matter

      Pages 127-127

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   2. General Notions

      • Nicola Cufaro Petroni

      Pages 129-143

   3. Heuristic Definitions

      • Nicola Cufaro Petroni

      Pages 145-182

   4. Markovianity

      • Nicola Cufaro Petroni

      Pages 183-223

   5. An Outline of Stochastic Calculus

      • Nicola Cufaro Petroni

      Pages 225-256

4. Physical Modeling

   1. Front Matter

      Pages 257-257

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   2. Dynamical Theory of Brownian Motion

      • Nicola Cufaro Petroni

      Pages 259-275

   3. Stochastic Mechanics

      • Nicola Cufaro Petroni

      Pages 277-299

5. Back Matter

   Pages 301-373

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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 Schrödinger 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.

• Probability for Physicists Textbook
• Markov Processes
• Brownian Motion
• Jump-Diffusion Processes
• Ito Calculus
• Stochastic Mechanics
• Stochastic Calculus
• Ornstein-Uhlenbeck Equations
• Stratonovich Integral

• Department of Physics, University of Bari, Bari, Italy

  Nicola Cufaro Petroni

Nicola Cufaro Petroni is a theoretical physicist and Associate Professor of Probability and Mathematical Statistics at the University of Bari (Italy). He is the author of over 80 publications in international journals and on various research topics: dynamics and control of stochastic processes; stochastic mechanics; entanglement of quantum states; foundations of quantum mechanics; Lévy processes and applications to physical systems; quantitative finance and Monte Carlo simulations; option pricing with jump-diffusion processes; control of the dynamics of charged particle beams in accelerators; neural networks and their applications; and recognition and classification of acoustic signals. He has taught a variety of courses in Probability and Theoretical Physics, including Probability and Statistics, Econophysics, Probabilistic Methods in Finance, and Mathematical Methods of Physics. He currently teaches Probabilistic Methods of Physics for the Master’s degree in Physics. 

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