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06869nam a2200925 4500 |
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ocn842307629 |
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OCoLC |
| 005 |
20170124071238.4 |
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m o d |
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cr ||||||||||| |
| 008 |
130501s2013 nju ob 001 0 eng |
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|a 2013017918
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|a DLC
|b eng
|e rda
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|z (OCoLC)961562671
|z (OCoLC)962644270
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|a pcc
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|x 003000
|2 bisacsh
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|a 519.2/82
|2 23
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|a MAT003000
|2 bisacsh
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|a MAIN
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| 100 |
1 |
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|a Ibe, Oliver C.
|q (Oliver Chukwudi),
|d 1947-
|
| 245 |
1 |
0 |
|a Elements of random walk and diffusion processes /
|c Oliver C. Ibe.
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| 264 |
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1 |
|a Hoboken, New Jersey :
|b Wiley,
|c [2013]
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| 300 |
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|a 1 online resource.
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| 336 |
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|a text
|2 rdacontent
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| 337 |
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|a computer
|2 rdamedia
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| 338 |
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|a online resource
|2 rdacarrier
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| 490 |
1 |
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|a Wiley series in operations research and management science.
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| 520 |
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|a "Featuring an introduction to stochastic calculus, this book uniquely blends diffusion equations and random walk theory and provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. It covers standard methods and applications of Brownian motion and discusses Levy motion; addresses fractional calculus; introduces percolation theory and its relationship to diffusion processes; and more"--
|c Provided by publisher.
|
| 520 |
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|a "This book features an introduction to powerful and general techniques that are used in the application of physical and dynamic processes and presents the connections between diffusion equations and random motion"--
|c Provided by publisher.
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| 504 |
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|a Includes bibliographical references and index.
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| 588 |
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|a Description based on print version record and CIP data provided by publisher.
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| 505 |
0 |
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|a Elements of Random Walk and Diffusion Processes; Copyright; Contents; Preface; Acknowledgments; 1 Review of Probability Theory; 1.1 Introduction; 1.2 Random Variables; 1.2.1 Distribution Functions; 1.2.2 Discrete Random Variables; 1.2.3 Continuous Random Variables; 1.2.4 Expectations; 1.2.5 Moments of Random Variables and the Variance; 1.3 Transform Methods; 1.3.1 The Characteristic Function; 1.3.2 Moment-Generating Property of the Characteristic Function; 1.3.3 The s-Transform; 1.3.4 Moment-Generating Property of the s-Transform; 1.3.5 The z-Transform.
|
| 505 |
8 |
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|a 1.3.6 Moment-Generating Property of the z-Transform1.4 Covariance and Correlation Coefficient; 1.5 Sums of Independent Random Variables; 1.6 Some Probability Distributions; 1.6.1 The Bernoulli Distribution; 1.6.2 The Binomial Distribution; 1.6.3 The Geometric Distribution; 1.6.4 The Poisson Distribution; 1.6.5 The Exponential Distribution; 1.6.6 Normal Distribution; 1.7 Limit Theorems; 1.7.1 Markov Inequality; 1.7.2 Chebyshev Inequality; 1.7.3 Laws of Large Numbers; 1.7.4 The Central Limit Theorem; Problems; 2 Overview of Stochastic Processes; 2.1 Introduction.
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| 505 |
8 |
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|a 2.2 Classification of Stochastic Processes2.3 Mean and Autocorrelation Function; 2.4 Stationary Processes; 2.4.1 Strict-Sense Stationary Processes; 2.4.2 Wide-Sense Stationary Processes; 2.5 Power Spectral Density; 2.6 Counting Processes; 2.7 Independent Increment Processes; 2.8 Stationary Increment Process; 2.9 Poisson Processes; 2.9.1 Compound Poisson Process; 2.10 Markov Processes; 2.10.1 Discrete-Time Markov Chains; 2.10.2 State Transition Probability Matrix; 2.10.3 The k-Step State Transition Probability; 2.10.4 State Transition Diagrams; 2.10.5 Classification of States.
|
| 505 |
8 |
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|a 2.10.6 Limiting-State Probabilities2.10.7 Doubly Stochastic Matrix; 2.10.8 Continuous-Time Markov Chains; 2.10.9 Birth and Death Processes; 2.11 Gaussian Processes; 2.12 Martingales; 2.12.1 Stopping Times; Problems; 3 One-Dimensional Random Walk; 3.1 Introduction; 3.2 Occupancy Probability; 3.3 Random Walk as a Markov Chain; 3.4 Symmetric Random Walk as a Martingale; 3.5 Random Walk with Barriers; 3.6 Mean-Square Displacement; 3.7 Gambler's Ruin; 3.7.1 Ruin Probability; 3.7.2 Alternative Derivation of Ruin Probability; 3.7.3 Duration of a Game; 3.8 Random Walk with Stay.
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| 505 |
8 |
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|a 3.9 First Return to the Origin3.10 First Passage Times for Symmetric Random Walk; 3.10.1 First Passage Time via the Generating Function; 3.10.2 First Passage Time via the Reflection Principle; 3.10.3 Hitting Time and the Reflection Principle; 3.11 The Ballot Problem and the Reflection Principle; 3.11.1 The Conditional Probability Method; 3.12 Returns to the Origin and the Arc-Sine Law; 3.13 Maximum of a Random Walk; 3.14 Two Symmetric Random Walkers; 3.15 Random Walk on a Graph; 3.15.1 Proximity Measures; 3.15.2 Directed Graphs; 3.15.3 Random Walk on an Undirected Graph.
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| 650 |
|
0 |
|a Random walks (Mathematics)
|
| 650 |
|
0 |
|a Diffusion processes.
|
| 650 |
|
7 |
|a MATHEMATICS / Applied.
|2 bisacsh
|
| 650 |
|
4 |
|a Diffusion processes.
|
| 650 |
|
4 |
|a MATHEMATICS
|x Applied.
|
| 650 |
|
4 |
|a Random walks (Mathematics)
|
| 650 |
|
7 |
|a Diffusion processes.
|2 fast
|0 (OCoLC)fst00893561
|
| 650 |
|
7 |
|a Random walks (Mathematics)
|2 fast
|0 (OCoLC)fst01089818
|
| 650 |
|
7 |
|a Stochastischer Prozess.
|2 gnd
|
| 650 |
|
7 |
|a Irrfahrtsproblem.
|2 gnd
|
| 650 |
|
7 |
|a Diffusionsprozess.
|2 gnd
|
| 655 |
|
4 |
|a Electronic books.
|
| 776 |
0 |
8 |
|i Print version:
|a Ibe, Oliver C. (Oliver Chukwudi), 1947-
|t Elements of random walk and diffusion processes
|d Hoboken, New Jersey : John Wiley & Sons, Inc., [2013]
|z 9781118618097
|w (DLC) 2013009389
|
| 830 |
|
0 |
|a Wiley series in operations research and management science.
|
| 856 |
4 |
0 |
|u https://doi.org/10.1002/9781118618059
|z Full Text via HEAL-Link
|
| 994 |
|
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|a 92
|b DG1
|
