國立高雄大學圖資館 |

Language: English

Back

Probability and stochastic processes...

Petroni, Nicola Cufaro.

Probability and stochastic processes for physicists

Record Type:	Electronic resources : Monograph/item
Title/Author:	Probability and stochastic processes for physicistsby Nicola Cufaro Petroni.
Author:	Petroni, Nicola Cufaro.
Published:	Cham :Springer International Publishing :2020.
Description:	xiii, 373 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Statistical physics.
Online resource:	https://doi.org/10.1007/978-3-030-48408-8
ISBN:	9783030484088$q(electronic bk.)

Probability and stochastic processes for physicists
Petroni, Nicola Cufaro.

Probability and stochastic processes for physicists[electronic resource] /by Nicola Cufaro Petroni. - Cham :Springer International Publishing :2020. - xiii, 373 p. :ill., digital ;24 cm. - UNITEXT for physics,2198-7882. - UNITEXT for 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)

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 Schrodinger 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.

ISBN: 9783030484088$q(electronic bk.)

Standard No.: 10.1007/978-3-030-48408-8doiSubjects--Topical Terms:

183716
Statistical physics.

LC Class. No.: QC174.8 / .P487 2020

Dewey Class. No.: 530.1595

Probability and stochastic processes for physicists
LDR:03339nmm a2200337 a 4500 001 580692
003 DE-He213
005 20201030165415.0
006 m
007 cr
008 210105s2020
020 $a 9783030484088$q(electronic bk.)
020 $a 9783030484071$q(paper)
024 7 $a 10.1007/978-3-030-48408-8 $2 doi
035 $a 978-3-030-48408-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.8 $b .P487 2020
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.1595 $2 23
090 $a QC174.8 $b .P497 2020
100 1 $a Petroni, Nicola Cufaro. $3 870615
245 1 0 $a Probability and stochastic processes for physicists $h [electronic resource] / $c by Nicola Cufaro Petroni.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xiii, 373 p. : $b ill., digital ; $c 24 cm.
490 1 $a UNITEXT for physics, $x 2198-7882
505 0 $a 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)
520 $a 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 Schrodinger 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.
650 0 $a Statistical physics. $3 183716
650 0 $a Stochastic processes. $3 181874
650 0 $a Mathematical physics. $3 190854
650 1 4 $a Mathematical Methods in Physics. $3 273796
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 376743
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Vibration, Dynamical Systems, Control. $3 274667
650 2 4 $a Quantum Physics. $3 275010
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a UNITEXT for physics. $3 681848
856 4 0 $u https://doi.org/10.1007/978-3-030-48408-8
950 $a Physics and Astronomy (Springer-11651)