Language:
English
繁體中文
Help
圖資館首頁
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
Probability theorya comprehensive co...
~
Klenke, Achim.
Probability theorya comprehensive course /
Record Type:
Electronic resources : Monograph/item
Title/Author:
Probability theoryby Achim Klenke.
Reminder of title:
a comprehensive course /
Author:
Klenke, Achim.
Published:
Cham :Springer International Publishing :2020.
Description:
xiv, 716 p. :ill., digital ;24 cm.
Contained By:
Springer Nature eBook
Subject:
Probabilities.
Online resource:
https://doi.org/10.1007/978-3-030-56402-5
ISBN:
9783030564025$q(electronic bk.)
Probability theorya comprehensive course /
Klenke, Achim.
Probability theory
a comprehensive course /[electronic resource] :by Achim Klenke. - Third edition. - Cham :Springer International Publishing :2020. - xiv, 716 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..
1 Basic Measure Theory -- 2 Independence -- 3 Generating Functions -- 4 The Integral -- 5 Moments and Laws of Large Numbers -- 6 Convergence Theorems -- 7 Lp-Spaces and the Radon-Nikodym Theorem -- 8 Conditional Expectations -- 9 Martingales -- 10 Optional Sampling Theorems -- 11 Martingale Convergence Theorems and Their Applications -- 12 Backwards Martingales and Exchangeability -- 13 Convergence of Measures -- 14 Probability Measures on Product Spaces -- 15 Characteristic Functions and the Central Limit Theorem -- 16 Infinitely Divisible Distributions -- 17 Markov Chains -- 18 Convergence of Markov Chains -- 19 Markov Chains and Electrical Networks -- 20 Ergodic Theory -- 21 Brownian Motion -- 22 Law of the Iterated Logarithm -- 23 Large Deviations -- 24 The Poisson Point Process -- 25 The Ito Integral -- 26 Stochastic Differential Equations -- References -- Notation Index -- Name Index -- Subject Index.
This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts. This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.
ISBN: 9783030564025$q(electronic bk.)
Standard No.: 10.1007/978-3-030-56402-5doiSubjects--Topical Terms:
182046
Probabilities.
LC Class. No.: QA273.18
Dewey Class. No.: 519.2
Probability theorya comprehensive course /
LDR
:03533nmm a2200361 a 4500
001
589012
003
DE-He213
005
20210204104511.0
006
m d
007
cr nn 008maaau
008
210525s2020 sz s 0 eng d
020
$a
9783030564025$q(electronic bk.)
020
$a
9783030564018$q(paper)
024
7
$a
10.1007/978-3-030-56402-5
$2
doi
035
$a
978-3-030-56402-5
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA273.18
072
7
$a
PBT
$2
bicssc
072
7
$a
MAT029000
$2
bisacsh
072
7
$a
PBT
$2
thema
072
7
$a
PBWL
$2
thema
082
0 4
$a
519.2
$2
23
090
$a
QA273.18
$b
.K64 2020
100
1
$a
Klenke, Achim.
$3
275733
245
1 0
$a
Probability theory
$h
[electronic resource] :
$b
a comprehensive course /
$c
by Achim Klenke.
250
$a
Third edition.
260
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2020.
300
$a
xiv, 716 p. :
$b
ill., digital ;
$c
24 cm.
490
1
$a
Universitext,
$x
0172-5939
505
0
$a
1 Basic Measure Theory -- 2 Independence -- 3 Generating Functions -- 4 The Integral -- 5 Moments and Laws of Large Numbers -- 6 Convergence Theorems -- 7 Lp-Spaces and the Radon-Nikodym Theorem -- 8 Conditional Expectations -- 9 Martingales -- 10 Optional Sampling Theorems -- 11 Martingale Convergence Theorems and Their Applications -- 12 Backwards Martingales and Exchangeability -- 13 Convergence of Measures -- 14 Probability Measures on Product Spaces -- 15 Characteristic Functions and the Central Limit Theorem -- 16 Infinitely Divisible Distributions -- 17 Markov Chains -- 18 Convergence of Markov Chains -- 19 Markov Chains and Electrical Networks -- 20 Ergodic Theory -- 21 Brownian Motion -- 22 Law of the Iterated Logarithm -- 23 Large Deviations -- 24 The Poisson Point Process -- 25 The Ito Integral -- 26 Stochastic Differential Equations -- References -- Notation Index -- Name Index -- Subject Index.
520
$a
This popular textbook, now in a revised and expanded third edition, presents a comprehensive course in modern probability theory. Probability plays an increasingly important role not only in mathematics, but also in physics, biology, finance and computer science, helping to understand phenomena such as magnetism, genetic diversity and market volatility, and also to construct efficient algorithms. Starting with the very basics, this textbook covers a wide variety of topics in probability, including many not usually found in introductory books, such as: limit theorems for sums of random variables martingales percolation Markov chains and electrical networks construction of stochastic processes Poisson point process and infinite divisibility large deviation principles and statistical physics Brownian motion stochastic integrals and stochastic differential equations. The presentation is self-contained and mathematically rigorous, with the material on probability theory interspersed with chapters on measure theory to better illustrate the power of abstract concepts. This third edition has been carefully extended and includes new features, such as concise summaries at the end of each section and additional questions to encourage self-reflection, as well as updates to the figures and computer simulations. With a wealth of examples and more than 290 exercises, as well as biographical details of key mathematicians, it will be of use to students and researchers in mathematics, statistics, physics, computer science, economics and biology.
650
0
$a
Probabilities.
$3
182046
650
1 4
$a
Probability Theory and Stochastic Processes.
$3
274061
650
2 4
$a
Measure and Integration.
$3
273777
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
Theoretical, Mathematical and Computational Physics.
$3
376743
710
2
$a
SpringerLink (Online service)
$3
273601
773
0
$t
Springer Nature eBook
830
0
$a
Universitext.
$3
558272
856
4 0
$u
https://doi.org/10.1007/978-3-030-56402-5
950
$a
Mathematics and Statistics (SpringerNature-11649)
based on 0 review(s)
ALL
電子館藏
Items
1 records • Pages 1 •
1
Inventory Number
Location Name
Item Class
Material type
Call number
Usage Class
Loan Status
No. of reservations
Opac note
Attachments
000000191549
電子館藏
1圖書
電子書
EB QA273.18 .K64 2020 2020
一般使用(Normal)
On shelf
0
1 records • Pages 1 •
1
Multimedia
Multimedia file
https://doi.org/10.1007/978-3-030-56402-5
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login