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Introduction to stochastic analysis : integrals and differential equations /
This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, ra...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London : Hoboken, NJ :
ISTE Ltd ; John Wiley,
2011.
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| Colección: | Applied stochastic methods series.
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| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
MARC
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| 100 | 1 | |a Mackevičius, Vigirdas. | |
| 245 | 1 | 0 | |a Introduction to stochastic analysis : |b integrals and differential equations / |c Vigirdas Mackevicius. |
| 260 | |a London : |b ISTE Ltd ; |a Hoboken, NJ : |b John Wiley, |c 2011. | ||
| 300 | |a 1 online resource (276 pages) : |b illustrations | ||
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| 490 | 1 | |a Applied stochastic methods series | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô's formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided. | ||
| 505 | 0 | |a Cover; Title Page; Copyright Page; Table of Contents; Preface; Notation; Chapter 1. Introduction: Basic Notions of Probability Theory; 1.1. Probability space; 1.2. Random variables; 1.3. Characteristics of a random variable; 1.4. Types of random variables; 1.5. Conditional probabilities and distributions; 1.6. Conditional expectations as random variables; 1.7. Independent events and random variables; 1.8. Convergence of random variables; 1.9. Cauchy criterion; 1.10. Series of random variables; 1.11. Lebesgue theorem; 1.12. Fubini theorem; 1.13. Random processes; 1.14. Kolmogorov theorem | |
| 505 | 8 | |a Chapter 2. Brownian Motion2.1. Definition and properties; 2.2. White noise and Brownian motion; 2.3. Exercises; Chapter 3. Stochastic Models with Brownian Motion and White Noise; 3.1. Discrete time; 3.2. Continuous time; Chapter 4. Stochastic Integral with Respect to Brownian Motion; 4.1. Preliminaries. Stochastic integral with respect to a step process; 4.2. Definition and properties; 4.3. Extensions; 4.4. Exercises; Chapter 5. Itô's Formula; 5.1. Exercises; Chapter 6. Stochastic Differential Equations; 6.1. Exercises; Chapter 7. Itô Processes; 7.1. Exercises | |
| 505 | 8 | |a Chapter 8. Stratonovich Integral and Equations8.1. Exercises; Chapter 9. Linear Stochastic Differential Equations; 9.1. Explicit solution of a linear SDE; 9.2. Expectation and variance of a solution of an LSDE; 9.3. Other explicitly solvable equations; 9.4. Stochastic exponential equation; 9.5. Exercises; Chapter 10. Solutions of SDEs as Markov Diffusion Processes; 10.1. Introduction; 10.2. Backward and forward Kolmogorov equations; 10.3. Stationary density of a diffusion process; 10.4. Exercises; Chapter 11. Examples; 11.1. Additive noise: Langevin equation | |
| 505 | 8 | |a 11.2. Additive noise: general case11.3. Multiplicative noise: general remarks; 11.4. Multiplicative noise: Verhulst equation; 11.5. Multiplicative noise: genetic model; Chapter 12. Example in Finance: Black-Scholes Model; 12.1. Introduction: what is an option?; 12.2. Self-financing strategies; 12.2.1. Portfolio and its trading strategy; 12.2.2. Self-financing strategies; 12.2.3. Stock discount; 12.3. Option pricing problem: the Black-Scholes model; 12.4. Black-Scholes formula; 12.5. Risk-neutral probabilities: alternative derivation of Black-Scholes formula; 12.6. Exercises | |
| 505 | 8 | |a Chapter 13. Numerical Solution of Stochastic Differential Equations13.1. Memories of approximations of ordinary differential equations; 13.2. Euler approximation; 13.3. Higher-order strong approximations; 13.4. First-order weak approximations; 13.5. Higher-order weak approximations; 13.6. Example: Milstein-type approximations; 13.7. Example: Runge-Kutta approximations; 13.8. Exercises; Chapter 14. Elements of Multidimensional Stochastic Analysis; 14.1. Multidimensional Brownian motion; 14.2. Itô's formula for a multidimensional Brownian motion; 14.3. Stochastic differential equations | |
| 590 | |a O'Reilly |b O'Reilly Online Learning: Academic/Public Library Edition | ||
| 650 | 0 | |a Stochastic analysis. | |
| 650 | 6 | |a Analyse stochastique. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Stochastic analysis |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Mackevicius, Vigirdas. |t Introduction to stochastic analysis. |d London : ISTE Ltd ; Hoboken, NJ : John Wiley, 2011 |z 9781848213111 |w (DLC) 2011012249 |w (OCoLC)711864615 |
| 830 | 0 | |a Applied stochastic methods series. | |
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