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A Basic Course in Probability Theory / / by Rabi Bhattacharya, Edward C. Waymire
| A Basic Course in Probability Theory / / by Rabi Bhattacharya, Edward C. Waymire |
| Autore | Bhattacharya Rabi |
| Edizione | [2nd ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (XII, 265 p.) |
| Disciplina | 519.2 |
| Collana | Universitext |
| Soggetto topico |
Probabilities
Measure theory Probability Theory and Stochastic Processes Measure and Integration |
| ISBN | 3-319-47974-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface to Second Edition -- Preface to First Edition -- I. Random Maps, Distribution, and Mathematical Expectation -- II. Independence, Conditional Expectation -- III. Martingales and Stopping Times -- IV. Classical Central Limit Theorems -- V. Classical Zero-One Laws, Laws of Large Numbers and Large Deviations -- VI. Fourier Series, Fourier Transform, and Characteristic Functions -- VII. Weak Convergence of Probability Measures on Metric Spaces -- VIII. Random Series of Independent Summands -- IX. Kolmogorov's Extension Theorem and Brownian Motion -- X. Brownian Motion: The LIL and Some Fine-Scale Properties -- XI. Strong Markov Property, Skorokhod Embedding and Donsker's Invariance Principle -- XII. A Historical Note on Brownian Motion -- XIII. Some Elements of the Theory of Markov Processes and their Convergence to Equilibrium -- A. Measure and Integration -- B. Topology and Function Spaces -- C. Hilbert Spaces and Applications in Measure Theory -- References -- Symbol Index -- Subject Index. |
| Record Nr. | UNINA-9910254079403321 |
Bhattacharya Rabi
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Continuous Parameter Markov Processes and Stochastic Differential Equations [[electronic resource] /] / by Rabi Bhattacharya, Edward C. Waymire
| Continuous Parameter Markov Processes and Stochastic Differential Equations [[electronic resource] /] / by Rabi Bhattacharya, Edward C. Waymire |
| Autore | Bhattacharya Rabi |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (502 pages) |
| Disciplina | 519.233 |
| Altri autori (Persone) | WaymireEdward C |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Probabilities
Mathematics Probability Theory Applications of Mathematics |
| ISBN | 3-031-33296-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. A review of Martingaels, stopping times and the Markov property -- 2. Semigroup theory and Markov processes.-3. Regularity of Markov process sample paths -- 4. Continuous parameter jump Markov processes -- 5. Processes with independent increments -- 6. The stochastic integral -- 7. Construction of difficusions as solutions of stochastic differential equations -- 8. Itô's Lemma -- 9. Cameron-Martin-Girsanov theorem -- 10. Support of nonsingular diffusions -- 11. Transience and recurrence of multidimensional diffusions -- 12. Criteria for explosion -- 13. Absorption, reflection and other transformations of Markov processes -- 14. The speed of convergence to equilibrium of discrete parameter Markov processes and Diffusions -- 15. Probabilistic representation of solutions to certain PDEs -- 16. Probabilistic solution of the classical Dirichlet problem -- 17. The functional Central Limit Theorem for ergodic Markov processes -- 18. Asymptotic stability for singular diffusions -- 19. Stochastic integrals with L2-Martingales -- 20. Local time for Brownian motion -- 21. Construction of one dimensional diffusions by Semigroups -- 22. Eigenfunction expansions of transition probabilities for one-dimensional diffusions -- 23. Special Topic: The Martingale Problem -- 24. Special topic: multiphase homogenization for transport in periodic media -- 25. Special topic: skew random walk and skew Brownian motion -- 26. Special topic: piecewise deterministic Markov processes in population biology -- A. The Hille-Yosida theorem and closed graph theorem -- References -- Related textbooks and monographs. |
| Record Nr. | UNINA-9910765490903321 |
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Bhattacharya Rabi
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Rabi N. Bhattacharya : Selected Papers / / edited by Manfred Denker, Edward C. Waymire
| Rabi N. Bhattacharya : Selected Papers / / edited by Manfred Denker, Edward C. Waymire |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 |
| Descrizione fisica | 1 online resource (717 p.) |
| Disciplina | 519.2 |
| Collana | Contemporary Mathematicians |
| Soggetto topico |
Probabilities
Statistics Probability Theory and Stochastic Processes Statistics for Business, Management, Economics, Finance, Insurance Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences |
| ISBN | 3-319-30190-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I: Modes of Approximation -- Hall, Contributions of Rabi Bhattacharya to the Central Limit Theory and Normal Approximation -- Yoshida, Asymptotic Expansions for Stochastic Processes -- Shao, An Introduction to Normal Approximation -- Reprints -- Part II: Large Time Asymptotics for Markov Processes I: Diffusion -- Varadhan, Martingale Methods for the Central Limit Theorem -- Kurtz, Ergodicity and Central Limit Theorems for Markov Processes -- Reprints -- Part III: Large Time Asymptotics for Markov Processes II: Dynamical Systems and Iterated Maps -- Athreya, Dynamical Systems, IID Random Iterations, and Markov Chains -- Waymire, Random Dynamical Systems and Selected Works of Rabi Bhattacharya -- Reprints -- Part IV: Stochastic Foundations in Applied Sciences I: Economics -- Kamihigashi, Stachurski, Stability Analysis for Random Dynamical Systems in Economics -- Roy, Some Economic Applications of Recent Advances in Random Dynamical Systems -- Reprints -- Part V: Stochastic Foundations in Applied Sciences II: Geophysics -- Thomann, Waymire, Advection-Dispersion in Fluid Media and Selected Works of Rabi Bhattacharya -- Flandoli, Romito, Cascade Representations for the Navier-Stokes Equations -- Reprints -- Part VI: Stochastic Foundations in Applied Sciences III: Statistics -- Dryden, Le, Preston, Wood, Nonparametric Statistical Methods on Manifolds -- Huckemann, Hotz, Nonparametric Statistics on Manifolds and Beyond -- Reprints. |
| Record Nr. | UNINA-9910254097403321 |
| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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