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Elements of random walk and diffusion processes [[electronic resource] /] / Oliver C. Ibe
| Elements of random walk and diffusion processes [[electronic resource] /] / Oliver C. Ibe |
| Autore | Ibe Oliver C (Oliver Chukwudi), <1947-> |
| Pubbl/distr/stampa | Hoboken, N.J., : John Wiley & Sons, Inc., 2013 |
| Descrizione fisica | 1 online resource (278 p.) |
| Disciplina | 519.2/82 |
| Collana | Wiley series in operations research and management science |
| Soggetto topico |
Random walks (Mathematics)
Diffusion processes |
| ISBN |
1-118-61793-2
1-118-61805-X 1-118-62985-X |
| Classificazione | MAT003000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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
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 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 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 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 3.15.4 Random Walk on a Weighted Graph |
| Record Nr. | UNINA-9910139012803321 |
Ibe Oliver C (Oliver Chukwudi), <1947->
|
||
| Hoboken, N.J., : John Wiley & Sons, Inc., 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elements of random walk and diffusion processes / / Oliver C. Ibe
| Elements of random walk and diffusion processes / / Oliver C. Ibe |
| Autore | Ibe Oliver C (Oliver Chukwudi), <1947-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : John Wiley & Sons, Inc., 2013 |
| Descrizione fisica | 1 online resource (278 p.) |
| Disciplina | 519.2/82 |
| Collana | Wiley series in operations research and management science |
| Soggetto topico |
Random walks (Mathematics)
Diffusion processes |
| ISBN |
1-118-61793-2
1-118-61805-X 1-118-62985-X |
| Classificazione | MAT003000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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
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 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 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 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 3.15.4 Random Walk on a Weighted Graph |
| Record Nr. | UNINA-9910817355103321 |
|
Ibe Oliver C (Oliver Chukwudi), <1947->
|
||
| Hoboken, N.J., : John Wiley & Sons, Inc., 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elements of the random walk : an introduction for advanced students and researchers / / Joseph Rudnick, George Gaspari [[electronic resource]]
| Elements of the random walk : an introduction for advanced students and researchers / / Joseph Rudnick, George Gaspari [[electronic resource]] |
| Autore | Rudnick Joseph Alan <1944-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2004 |
| Descrizione fisica | 1 online resource (xv, 329 pages) : digital, PDF file(s) |
| Disciplina | 519.2/82 |
| Soggetto topico | Random walks (Mathematics) |
| ISBN |
1-107-14767-0
1-282-39477-0 9786612394775 0-511-64435-3 0-511-64813-8 0-511-18750-5 0-511-56649-2 0-511-61091-2 0-511-18657-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; 1 Introduction to techniques; 2 Generating functions I; 3 Generating functions II: recurrence, sites visited, and the role of dimensionality; 4 Boundary conditions, steady state, and the electrostatic analogy; 5 Variations on the random walk; 6 The shape of a random walk; 7 Path integrals and self-avoidance; 8 Properties of the random walk: introduction to scaling; 9 Scaling of walks and critical phenomena; 10 Walks and the O(n) model: mean field theory and spin waves; 11 Scaling, fractals, and renormalization
12 More on the renormalization groupReferences; Index |
| Record Nr. | UNINA-9910457872203321 |
|
Rudnick Joseph Alan <1944->
|
||
| Cambridge : , : Cambridge University Press, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elements of the random walk : an introduction for advanced students and researchers / / Joseph Rudnick, George Gaspari [[electronic resource]]
| Elements of the random walk : an introduction for advanced students and researchers / / Joseph Rudnick, George Gaspari [[electronic resource]] |
| Autore | Rudnick Joseph Alan <1944-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2004 |
| Descrizione fisica | 1 online resource (xv, 329 pages) : digital, PDF file(s) |
| Disciplina | 519.2/82 |
| Soggetto topico | Random walks (Mathematics) |
| ISBN |
1-107-14767-0
1-282-39477-0 9786612394775 0-511-64435-3 0-511-64813-8 0-511-18750-5 0-511-56649-2 0-511-61091-2 0-511-18657-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; 1 Introduction to techniques; 2 Generating functions I; 3 Generating functions II: recurrence, sites visited, and the role of dimensionality; 4 Boundary conditions, steady state, and the electrostatic analogy; 5 Variations on the random walk; 6 The shape of a random walk; 7 Path integrals and self-avoidance; 8 Properties of the random walk: introduction to scaling; 9 Scaling of walks and critical phenomena; 10 Walks and the O(n) model: mean field theory and spin waves; 11 Scaling, fractals, and renormalization
12 More on the renormalization groupReferences; Index |
| Record Nr. | UNINA-9910784439303321 |
|
Rudnick Joseph Alan <1944->
|
||
| Cambridge : , : Cambridge University Press, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elements of the random walk : an introduction for advanced students and researchers / / Joseph Rudnick, George Gaspari [[electronic resource]]
| Elements of the random walk : an introduction for advanced students and researchers / / Joseph Rudnick, George Gaspari [[electronic resource]] |
| Autore | Rudnick Joseph Alan <1944-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2004 |
| Descrizione fisica | 1 online resource (xv, 329 pages) : digital, PDF file(s) |
| Disciplina | 519.2/82 |
| Soggetto topico | Random walks (Mathematics) |
| ISBN |
1-107-14767-0
1-282-39477-0 9786612394775 0-511-64435-3 0-511-64813-8 0-511-18750-5 0-511-56649-2 0-511-61091-2 0-511-18657-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; 1 Introduction to techniques; 2 Generating functions I; 3 Generating functions II: recurrence, sites visited, and the role of dimensionality; 4 Boundary conditions, steady state, and the electrostatic analogy; 5 Variations on the random walk; 6 The shape of a random walk; 7 Path integrals and self-avoidance; 8 Properties of the random walk: introduction to scaling; 9 Scaling of walks and critical phenomena; 10 Walks and the O(n) model: mean field theory and spin waves; 11 Scaling, fractals, and renormalization
12 More on the renormalization groupReferences; Index |
| Record Nr. | UNINA-9910819265703321 |
|
Rudnick Joseph Alan <1944->
|
||
| Cambridge : , : Cambridge University Press, , 2004 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
First steps in random walks [[electronic resource] ] : from tools to applications / / J. Klafter and I.M. Sokolov
| First steps in random walks [[electronic resource] ] : from tools to applications / / J. Klafter and I.M. Sokolov |
| Autore | Klafter J (Joseph) |
| Pubbl/distr/stampa | Oxford, : Oxford University Press, 2011 |
| Descrizione fisica | 1 online resource (161 p.) |
| Disciplina | 519.2/82 |
| Altri autori (Persone) | SokolovIgor M. <1958-> |
| Soggetto topico | Random walks (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-299-48624-X
0-19-155295-X 0-19-177502-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Characteristic functions -- 2. Generating functions and applications -- 3. Continuous-time random walks -- 4. CTRW and aging phenomena -- 5. Master equations -- 6. Fractional diffusion and Fokker-Planck equations for subdiffusion -- 7. Lévy flights -- 8. Coupled CTRW and Lévy walks -- 9. Simple reactions : A+B->B -- 10. Random walks on percolation structures. |
| Record Nr. | UNINA-9910453016303321 |
|
Klafter J (Joseph)
|
||
| Oxford, : Oxford University Press, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
First steps in random walks [[electronic resource] ] : from tools to applications / / J. Klafter and I.M. Sokolov
| First steps in random walks [[electronic resource] ] : from tools to applications / / J. Klafter and I.M. Sokolov |
| Autore | Klafter J (Joseph) |
| Pubbl/distr/stampa | Oxford, : Oxford University Press, 2011 |
| Descrizione fisica | vi, 152 p. : ill |
| Disciplina | 519.2/82 |
| Altri autori (Persone) | SokolovIgor M. <1958-> |
| Soggetto topico | Random walks (Mathematics) |
| ISBN |
0-19-155295-X
0-19-177502-9 1-299-48624-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Characteristic functions -- 2. Generating functions and applications -- 3. Continuous-time random walks -- 4. CTRW and aging phenomena -- 5. Master equations -- 6. Fractional diffusion and Fokker-Planck equations for subdiffusion -- 7. Levy flights -- 8. Coupled CTRW and Levy walks -- 9. Simple reactions : A+B->B -- 10. Random walks on percolation structures. |
| Record Nr. | UNINA-9910795854203321 |
|
Klafter J (Joseph)
|
||
| Oxford, : Oxford University Press, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
First steps in random walks : from tools to applications / / J. Klafter and I.M. Sokolov
| First steps in random walks : from tools to applications / / J. Klafter and I.M. Sokolov |
| Autore | Klafter J (Joseph) |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Oxford, : Oxford University Press, 2011 |
| Descrizione fisica | vi, 152 p. : ill |
| Disciplina | 519.2/82 |
| Altri autori (Persone) | SokolovIgor M. <1958-> |
| Soggetto topico | Random walks (Mathematics) |
| ISBN |
0-19-155295-X
0-19-177502-9 1-299-48624-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. Characteristic functions -- 2. Generating functions and applications -- 3. Continuous-time random walks -- 4. CTRW and aging phenomena -- 5. Master equations -- 6. Fractional diffusion and Fokker-Planck equations for subdiffusion -- 7. Levy flights -- 8. Coupled CTRW and Levy walks -- 9. Simple reactions : A+B->B -- 10. Random walks on percolation structures. |
| Record Nr. | UNINA-9910818844103321 |
|
Klafter J (Joseph)
|
||
| Oxford, : Oxford University Press, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Moderate deviations for the range of planar random walks / / Richard F. Bass, Xia Chen, Jay Rosen
| Moderate deviations for the range of planar random walks / / Richard F. Bass, Xia Chen, Jay Rosen |
| Autore | Bass Richard F. |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (82 p.) |
| Disciplina | 519.2/82 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Random walks (Mathematics)
Deviation (Mathematics) Local times (Stochastic processes) Limit theorems (Probability theory) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0535-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. History""; ""Chapter 3. Overview""; ""Chapter 4. Preliminaries""; ""Chapter 5. Moments of the range""; ""Chapter 6. Moderate deviations for R[sub(n)] � ER[sub(n)]""; ""Chapter 7. Moderate deviations for ER[sub(n)] � R[sub(n)]""; ""Chapter 8. Exponential asymptotics for the smoothed range""; ""Chapter 9. Exponential approximation""; ""Chapter 10. Laws of the iterated logarithm""; ""Bibliography"" |
| Record Nr. | UNINA-9910480247503321 |
|
Bass Richard F.
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Moderate deviations for the range of planar random walks / / Richard F. Bass, Xia Chen, Jay Rosen
| Moderate deviations for the range of planar random walks / / Richard F. Bass, Xia Chen, Jay Rosen |
| Autore | Bass Richard F. |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (82 p.) |
| Disciplina | 519.2/82 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Random walks (Mathematics)
Deviation (Mathematics) Local times (Stochastic processes) Limit theorems (Probability theory) |
| ISBN | 1-4704-0535-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. History""; ""Chapter 3. Overview""; ""Chapter 4. Preliminaries""; ""Chapter 5. Moments of the range""; ""Chapter 6. Moderate deviations for R[sub(n)] � ER[sub(n)]""; ""Chapter 7. Moderate deviations for ER[sub(n)] � R[sub(n)]""; ""Chapter 8. Exponential asymptotics for the smoothed range""; ""Chapter 9. Exponential approximation""; ""Chapter 10. Laws of the iterated logarithm""; ""Bibliography"" |
| Record Nr. | UNINA-9910788854803321 |
|
Bass Richard F.
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
