05178cam a2200553Mi 4500 ocn828298898 OCoLC 20171107093446.0 m o d cr cnu|||unuuu 130223s2013 enk o 000 0 eng d 9781118603338 (electronic bk.) 1118603338 (electronic bk.) 9781118603246 1118603249 DEBSZ 39748044X DEBSZ 431339252 DEBSZ 449346781 NZ1 15916046 DEBBG BV043395465 (OCoLC)828298898 EBLCP eng pn EBLCP YDXCP DG1 DEBSZ OCLCQ OCLCA OCLCF OCLCQ DEBBG MAIN QA274.2 .M33 2011 519.2/2 519.22 Mackevičius, Vigirdas. Introduction to stochastic analysis : integrals and differential equations / Vigirdas Mackevičius. [electronic resource] London : Wiley, 2013. 1 online resource (278 pages). text txt rdacontent computer c rdamedia online resource cr rdacarrier ISTE 14.4. Itô processes. 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. 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. 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. 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. 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. 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. Print version record. Stochastic analysis. Stochastic analysis. fast (OCoLC)fst01133499 Electronic books. Print version: Mackevicius, Vigirdas. Introduction to Stochastic Analysis : Integrals and Differential Equations. London : Wiley, ©2013 9781848213111 ISTE. http://onlinelibrary.wiley.com/book/10.1002/9781118603338 Wiley Online Library ddc BK 206471 206471