Catalogue des documents imprimés de la bibliothèque
Normal view MARC view

Probability and Stochastic Processes for Physicists / by Nicola Cufaro Petroni

Ouvrage
Auteur principal: Cufaro Petroni, Nicola, AuteurLangue : anglaisPays : Allemagne.Mention d'édition: 1st ed. 2020.Publication : Cham : Springer International Publishing, 2020ISBN : 9783030484088.Collection: UNITEXT for Physics, 2198-7890Note de contenu : 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) Résumé : 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..Sujet - Nom commun: Physics | Probabilities | Mathematical physics | Dynamics | Ergodic theory | Vibration | Dynamical systems | Quantum physics Catégorie de sujet: Physics and Astronomy Ressources en ligne :Cliquez ici pour consulter en ligne | Livre électronique
Holdings
Item type Current library Call number Status Date due Barcode
Ouvrage Ouvrage La bibliothèque de l'ESPCI Salle de lecture ST-008 (Browse shelf(Opens below)) Available ST-008

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).

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.

Nécessite un lecteur de fichier PDF

L'accès complet à la ressource est réservé aux usagers des établissements qui en ont fait l'acquisition