東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Probability and stochastic processes...

Petroni, Nicola Cufaro.

Linked to FindBook

Google Book

Amazon

博客來

Probability and stochastic processes for physicists

Record Type:	Electronic resources : Monograph/item
Title/Author:	Probability and stochastic processes for physicists/ by Nicola Cufaro Petroni.
Author:	Petroni, Nicola Cufaro.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xiii, 373 p. :ill., digital ;24 cm.
[NT 15003449]:	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)
Contained By:	Springer eBooks
Subject:	Statistical physics. -
Online resource:	https://doi.org/10.1007/978-3-030-48408-8
ISBN:	9783030484088

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

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

536281
Statistical physics.

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

Dewey Class. No.: 530.1595

Probability and stochastic processes for physicists
LDR:03397nmm a2200337 a 4500 001 2221357
003 DE-He213
005 20201030165415.0
006 m d
007 cr nn 008maaau
008 201216s2020 sz s 0 eng d
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 3459553
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 536281
650 0 $a Stochastic processes. $3 520663
650 0 $a Mathematical physics. $3 516853
650 1 4 $a Mathematical Methods in Physics. $3 890898
650 2 4 $a Probability Theory and Stochastic Processes. $3 891080
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 1066859
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Vibration, Dynamical Systems, Control. $3 893843
650 2 4 $a Quantum Physics. $3 893952
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a UNITEXT for physics. $3 2068732
856 4 0 $u https://doi.org/10.1007/978-3-030-48408-8
950 $a Physics and Astronomy (Springer-11651)