Applied stochastic analysis / Weinan E, Tiejun Li, Eric Vanden-Eijnden

By:

E, Weinan, 1963- [VerfasserIn]

Contributor(s):

Resource type: Ressourcentyp: BuchBookLanguage: English Series: Graduate studies in mathematics ; 199Publisher: Providence, Rhode Island : American Mathematical Society, [2019]Copyright date: © 2019Description: xxi, 305 Seiten : Illustrationen, DiagrammeISBN:

9781470449339

Subject(s):

Additional physical formats: 9781470452414 | Erscheint auch als: Applied stochastic analysis. Online-Ausgabe Providence, Rhode Island : American Mathematical Society, 2019. 1 Online-Ressource (xxi, 305 Seiten)DDC classification:

519.2

MSC: MSC: 60-01 | 62P35 | 65C05 | 65C10 | 82-01 | *60-01 | 60J22 | 60H10 | 60H35 | 62P10RVK: RVK: SK 820LOC classification:

QA274.2

Summary: This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.Summary: Cover -- Title page -- Introduction to the Series -- Preface -- Notation -- Part 1 . Fundamentals -- Chapter 1. Random Variables -- 1.1. Elementary Examples -- 1.2. Probability Space -- 1.3. Conditional Probability -- 1.4. Discrete Distributions -- 1.5. Continuous Distributions -- 1.6. Independence -- 1.7. Conditional Expectation -- 1.8. Notions of Convergence -- 1.9. Characteristic Function -- 1.10. Generating Function and Cumulants -- 1.11. The Borel-Cantelli Lemma -- Exercises -- Notes -- Chapter 2. Limit Theorems -- 2.1. The Law of Large Numbers -- 2.2. Central Limit Theorem -- 2.3. Cramér's Theorem for Large Deviations -- 2.4. Statistics of Extrema -- Exercises -- Notes -- Chapter 3. Markov Chains -- 3.1. Discrete Time Finite Markov Chains -- 3.2. Invariant Distribution -- 3.3. Ergodic Theorem for Finite Markov Chains -- 3.4. Poisson Processes -- 3.5. -processes -- 3.6. Embedded Chain and Irreducibility -- 3.7. Ergodic Theorem for -processes -- 3.8. Time Reversal -- 3.9. Hidden Markov Model -- 3.10. Networks and Markov Chains -- Exercises -- Notes -- Chapter 4. Monte Carlo Methods -- 4.1. Numerical Integration -- 4.2. Generation of Random Variables -- 4.3. Variance Reduction -- 4.4. The Metropolis Algorithm -- 4.5. Kinetic Monte Carlo -- 4.6. Simulated Tempering -- 4.7. Simulated Annealing -- Exercises -- Notes -- Chapter 5. Stochastic Processes -- 5.1. Axiomatic Construction of Stochastic Process -- 5.2. Filtration and Stopping Time -- 5.3. Markov Processes -- 5.4. Gaussian Processes -- Exercises -- Notes -- Chapter 6. Wiener Process -- 6.1. The Diffusion Limit of Random Walks -- 6.2. The Invariance Principle -- 6.3. Wiener Process as a Gaussian Process -- 6.4. Wiener Process as a Markov Process -- 6.5. Properties of the Wiener Process -- 6.6. Wiener Process under Constraints -- 6.7. Wiener Chaos Expansion -- Exercises -- Notes.PPN: PPN: 1664213570

Holdings ( 1 )

Holdings
Item type	Home library	Shelving location	Call number	Status	Date due	Barcode	Item holds
Freihandbestand ausleihbar	Fachbibliothek Mathematik	Bibliothek / frei aufgestellt	Stoch. / Wei	Available		36595597090

Total holds: 0