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Physics of stochastic processes : how randomness acts in time / / by Reinhard Mahnke, Jevgenijs Kaupuzs, Ihor Lubashevsky
| Physics of stochastic processes : how randomness acts in time / / by Reinhard Mahnke, Jevgenijs Kaupuzs, Ihor Lubashevsky |
| Autore | Mahnke R (Reinhard) |
| Pubbl/distr/stampa | Weinheim, : Wiley-VCH, 2009 |
| Descrizione fisica | 1 online resource (450 p.) |
| Disciplina | 519.23 |
| Altri autori (Persone) |
KaupuzsJevgenijs
LubashevskiiI. A (Igor' Alekseevich) |
| Collana | Physics textbook |
| Soggetto topico |
Random measures
Statistical physics Stochastic processes |
| ISBN |
1-282-27959-9
9786612279591 3-527-62609-3 3-527-62610-7 |
| Classificazione |
417.1
519.23 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Physics of Stochastic Processes; Contents; Preface; Part I Basic Mathematical Description; 1 Fundamental Concepts; 1.1 Wiener Process, Adapted Processes and Quadratic Variation; 1.2 The Space of Square Integrable Random Variables; 1.3 The Ito Integral and the Ito Formula; 1.4 The Kolmogorov Differential Equation and the Fokker-Planck Equation; 1.5 Special Diffusion Processes; 1.6 Exercises; 2 Multidimensional Approach; 2.1 Bounded Multidimensional Region; 2.2 From Chapman-Kolmogorov Equation to Fokker-Planck Description; 2.2.1 The Backward Fokker-Planck Equation; 2.2.2 Boundary Singularities
2.2.3 The Forward Fokker-Planck Equation2.2.4 Boundary Relations; 2.3 Different Types of Boundaries; 2.4 Equivalent Lattice Representation of Random Walks Near the Boundary; 2.4.1 Diffusion Tensor Representations; 2.4.2 Equivalent Lattice Random Walks; 2.4.3 Properties of the Boundary Layer; 2.5 Expression for Boundary Singularities; 2.6 Derivation of Singular Boundary Scaling Properties; 2.6.1 Moments of the Walker Distribution and the Generating Function; 2.6.2 Master Equation for Lattice Random Walks and its General Solution; 2.6.3 Limit of Multiple-Step Random Walks on Small Time Scales 2.6.4 Continuum Limit and a Boundary Model2.7 Boundary Condition for the Backward Fokker-Planck Equation; 2.8 Boundary Condition for the Forward Fokker-Planck Equation; 2.9 Concluding Remarks; 2.10 Exercises; Part II Physics of Stochastic Processes; 3 The Master Equation; 3.1 Markovian Stochastic Processes; 3.2 The Master Equation; 3.3 One-Step Processes in Finite Systems; 3.4 The First-Passage Time Problem; 3.5 The Poisson Process in Closed and Open Systems; 3.6 The Two-Level System; 3.7 The Three-Level System; 3.8 Exercises; 4 The Fokker-Planck Equation; 4.1 General Fokker-Planck Equations 4.2 Bounded Drift-Diffusion in One Dimension4.3 The Escape Problem and its Solution; 4.4 Derivation of the Fokker-Planck Equation; 4.5 Fokker-Planck Dynamics in Finite State Space; 4.6 Fokker-Planck Dynamics with Coordinate-Dependent Diffusion Coefficient; 4.7 Alternative Method of Solving the Fokker-Planck Equation; 4.8 Exercises; 5 The Langevin Equation; 5.1 A System of Many Brownian Particles; 5.2 A Traditional View of the Langevin Equation; 5.3 Additive White Noise; 5.4 Spectral Analysis; 5.5 Brownian Motion in Three-Dimensional Velocity Space; 5.6 Stochastic Differential Equations 5.7 The Standard Wiener Process5.8 Arithmetic Brownian Motion; 5.9 Geometric Brownian Motion; 5.10 Exercises; Part III Applications; 6 One-Dimensional Diffusion; 6.1 Random Walk on a Line and Diffusion: Main Results; 6.2 A Drunken Sailor as Random Walker; 6.3 Diffusion with Natural Boundaries; 6.4 Diffusion in a Finite Interval with Mixed Boundaries; 6.5 The Mirror Method and Time Lag; 6.6 Maximum Value Distribution; 6.7 Summary of Results for Diffusion in a Finite Interval; 6.7.1 Reflected Diffusion; 6.7.2 Diffusion in a Semi-Open System; 6.7.3 Diffusion in an Open System; 6.8 Exercises 7 Bounded Drift-Diffusion Motion |
| Record Nr. | UNINA-9910139764203321 |
Mahnke R (Reinhard)
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| Weinheim, : Wiley-VCH, 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Probability and statistical inference / / Robert Bartoszynski, Magdalena Niewiadomska-Bugaj
| Probability and statistical inference / / Robert Bartoszynski, Magdalena Niewiadomska-Bugaj |
| Autore | Bartoszynski Robert |
| Edizione | [3rd ed] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2021] |
| Descrizione fisica | 1 online resource (595 pages) |
| Disciplina | 519.54 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico | Probabilities |
| ISBN |
1-119-24381-5
1-119-24382-3 1-119-24383-1 |
| Classificazione |
417.1
519.54 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- Preface to Third Edition -- Preface to Second Edition -- About the Companion Website -- Chapter 1 Experiments, Sample Spaces, and Events -- 1.1 Introduction -- 1.2 Sample Space -- 1.3 Algebra of Events -- 1.4 Infinite Operations on Events -- Chapter 2 Probability -- 2.1 Introduction -- 2.2 Probability as a Frequency -- 2.3 Axioms of Probability -- 2.4 Consequences of the Axioms -- 2.5 Classical Probability -- 2.6 Necessity of the Axioms* -- 2.7 Subjective Probability* -- Chapter 3 Counting -- 3.1 Introduction -- 3.2 Product Sets, Orderings, and Permutations -- 3.3 Binomial Coefficients -- 3.4 Multinomial Coefficients -- Chapter 4 Conditional Probability, Independence, and Markov Chains -- 4.1 Introduction -- 4.2 Conditional Probability -- 4.3 Partitions -- Total Probability Formula -- 4.4 Bayes' Formula -- 4.5 Independence -- 4.6 Exchangeability -- Conditional Independence -- 4.7 Markov Chains* -- Chapter 5 Random Variables: Univariate Case -- 5.1 Introduction -- 5.2 Distributions of Random Variables -- 5.3 Discrete and Continuous Random Variables -- 5.4 Functions of Random Variables -- 5.5 Survival and Hazard Functions -- Chapter 6 Random Variables: Multivariate Case -- 6.1 Bivariate Distributions -- 6.2 Marginal Distributions -- Independence -- 6.3 Conditional Distributions -- 6.4 Bivariate Transformations -- 6.5 Multidimensional Distributions -- Chapter 7 Expectation -- 7.1 Introduction -- 7.2 Expected Value -- 7.3 Expectation as an Integral* -- Riemann Integral -- Lebesque Integral -- Riemann-Stieltjes Integral -- Lebesque-Stieltjes Integral -- Lebesque Integral: General Case -- 7.4 Properties of Expectation -- 7.5 Moments -- 7.6 Variance -- 7.7 Conditional Expectation -- 7.8 Inequalities -- Chapter 8 Selected Families of Distributions -- 8.1 Bernoulli Trials and Related Distributions.
Binomial Distribution -- Geometric Distribution -- Negative Binomial Distribution -- 8.2 Hypergeometric Distribution -- 8.3 Poisson Distribution and Poisson Process -- 8.4 Exponential, Gamma, and Related Distributions -- 8.5 Normal Distribution -- 8.6 Beta Distribution -- Chapter 9 Random Samples -- 9.1 Statistics and Sampling Distributions -- 9.2 Distributions Related to Normal -- 9.3 Order Statistics -- 9.4 Generating Random Samples -- 9.5 Convergence -- Weak Laws of Large Numbers -- Strong Laws of Large Numbers -- 9.6 Central Limit Theorem -- Chapter 10 Introduction to Statistical Inference -- 10.1 Overview -- 10.2 Basic Models -- 10.3 Sampling -- 10.4 Measurement Scales -- Chapter 11 Estimation -- 11.1 Introduction -- 11.2 Consistency -- 11.3 Loss, Risk, and Admissibility -- 11.4 Efficiency -- 11.5 Methods of Obtaining Estimators -- Method of Moments Estimators -- Maximum Likelihood Estimators -- Least Squares Estimators -- Robust Estimators -- 11.6 Sufficiency -- 11.7 Interval Estimation -- Confidence Intervals -- Bootstrap Intervals -- Chapter 12 Testing Statistical Hypotheses -- 12.1 Introduction -- 12.2 Intuitive Background -- 12.3 Most Powerful Tests -- 12.4 Uniformly Most Powerful Tests -- 12.5 Unbiased Tests -- 12.6 Generalized Likelihood Ratio Tests -- 12.7 Conditional Tests -- 12.8 Tests and Confidence Intervals -- 12.9 Review of Tests for Normal Distributions -- One‐Sample Procedures -- Hypotheses About the Variance, Mean Known -- Hypotheses About the Variance, Mean Unknown -- Two‐Sample Procedures -- Large Sample Tests for Binomial Distribution -- 12.10 Monte Carlo, Bootstrap, and Permutation Tests -- Monte Carlo Tests -- Bootstrap Tests -- Permutation Tests -- Chapter 13 Linear Models -- 13.1 Introduction -- 13.2 Regression of the First and Second Kind -- 13.3 Distributional Assumptions -- 13.4 Linear Regression in the Normal Case. 13.5 Testing Linearity -- 13.6 Prediction -- 13.7 Inverse Regression -- 13.8 BLUE -- 13.9 Regression Toward the Mean -- 13.10 Analysis of Variance -- 13.11 One‐Way Layout -- 13.12 Two‐Way Layout -- 13.13 ANOVA Models with Interaction -- 13.14 Further Extensions -- Chapter 14 Rank Methods -- 14.1 Introduction -- 14.2 Glivenko-Cantelli Theorem -- 14.3 Kolmogorov-Smirnov Tests -- One‐Sample Kolmogorov-Smirnov Test -- Two‐Sample Kolmogorov-Smirnov Test -- 14.4 One‐Sample Rank Tests -- 14.5 Two‐Sample Rank Tests -- 14.6 Kruskal-Wallis Test -- Chapter 15 Analysis of Categorical Data -- 15.1 Introduction -- 15.2 Chi‐Square Tests -- 15.3 Homogeneity and Independence -- 15.4 Consistency and Power -- 15.5 2 × 2 Contingency Tables -- 15.6 r×c Contingency Tables -- Chapter 16 Basics of Bayesian Statistics -- 16.1 Introduction -- 16.2 Prior and Posterior Distributions -- 16.3 Bayesian Inference -- Predictive Distribution -- Point Estimation -- Bayesian Intervals -- Bayesian Hypotheses Testing -- 16.4 Final Comments -- Appendix A Supporting R Code -- Appendix B Statistical Tables -- Bibliography -- Answers to Odd‐Numbered Problems -- Index -- EULA. |
| Record Nr. | UNINA-9910830705603321 |
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Bartoszynski Robert
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| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probability and stochastic processes / / Ionut Florescu, Stevens Institute of Technology, Hoboken, NJ
| Probability and stochastic processes / / Ionut Florescu, Stevens Institute of Technology, Hoboken, NJ |
| Autore | Florescu Ionut <1973-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2015] |
| Descrizione fisica | 1 online resource (579 pages) : illustrations |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities
Stochastic processes |
| ISBN |
1-118-59313-8
1-118-59320-0 |
| Classificazione |
417.1
519.2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910795953803321 |
|
Florescu Ionut <1973->
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2015] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probability and stochastic processes / / Ionut Florescu, Stevens Institute of Technology, Hoboken, NJ
| Probability and stochastic processes / / Ionut Florescu, Stevens Institute of Technology, Hoboken, NJ |
| Autore | Florescu Ionut <1973-> |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2015] |
| Descrizione fisica | 1 online resource (579 pages) : illustrations |
| Disciplina | 519.2 |
| Soggetto topico |
Probabilities
Stochastic processes |
| ISBN |
1-118-59313-8
1-118-59320-0 |
| Classificazione |
417.1
519.2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910809023503321 |
|
Florescu Ionut <1973->
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2015] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stochastic numerical methods : an introduction for students and scientists / / Raul Toral and Pere Colet
| Stochastic numerical methods : an introduction for students and scientists / / Raul Toral and Pere Colet |
| Autore | Toral Raul |
| Pubbl/distr/stampa | Weinheim, Germany : , : Wiley-VCH, , 2014 |
| Descrizione fisica | 1 online resource (419 pages) |
| Disciplina | 519.2 |
| Collana | Physics textbook |
| Soggetto topico | Stochastic processes - Mathematical models |
| ISBN |
3-527-68314-3
3-527-68313-5 3-527-68312-7 |
| Classificazione |
417.1
519.2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910796091003321 |
|
Toral Raul
|
||
| Weinheim, Germany : , : Wiley-VCH, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Stochastic numerical methods : an introduction for students and scientists / / Raul Toral and Pere Colet
| Stochastic numerical methods : an introduction for students and scientists / / Raul Toral and Pere Colet |
| Autore | Toral Raul |
| Pubbl/distr/stampa | Weinheim, Germany : , : Wiley-VCH, , 2014 |
| Descrizione fisica | 1 online resource (419 pages) |
| Disciplina | 519.2 |
| Collana | Physics textbook |
| Soggetto topico | Stochastic processes - Mathematical models |
| ISBN |
3-527-68314-3
3-527-68313-5 3-527-68312-7 |
| Classificazione |
417.1
519.2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910808571803321 |
|
Toral Raul
|
||
| Weinheim, Germany : , : Wiley-VCH, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||