Probability and Stochastic Processes for Physicists

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.

• Part 1: Probability.- Chapter 1. Probability spaces.- Chapter 2. Distributions.- Chapter 3. Random variables.- Chapter 4. Limit theorems.- Part 2: Stochastic Processes.- Chapter 5. General notions.- Chapter 6. Heuristic definitions.- Chapter 7. Markovianity.- Chapter 8. An outline of stochastic calculus.- Part 3: Physical modeling.- Chapter 9. Dynamical theory of Brownian motion.- Chapter 10. Stochastic mechanics.- Part 4: Appendices .- A Consistency (Sect. 2.3.4).- B Inequalities (Sect. 3.3.2).- C Bertrand’s paradox (Sect. 3.5.1).- D Lp spaces of rv’s (Sect. 4.1).- E Moments and cumulants (Sect. 4.2.1).- F Binomial limit theorems (Sect. 4.3).- G Non uniform point processes (Sect 6.1.1).- H Stochastic calculus paradoxes (Sect. 6.4.2).- I Pseudo-Markovian processes (Sect. 7.1.2).- J Fractional Brownian motion (Sect. 7.1.10) .- K Ornstein-Uhlenbeck equations (Sect. 7.2.4).- L Stratonovich integral (Sect. 8.2.2).- M Stochastic bridges (Sect. 10.2).- N Kinematics of Gaussian diffusions (Sect. 10.3.1).- O Substantial operators (Sect. 10.3.3).- P Constant diffusion coefficients (Sect. 10.4).