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Introduction to stochastic analysis : (Record no. 20177)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05154cam a2200565Mi 4500 |
| 001 - CONTROL NUMBER | |
| control field | ocn828298898 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20230823095530.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||unuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 130223s2013 enk o 000 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | EBLCP |
| Language of cataloging | eng |
| Description conventions | pn |
| Transcribing agency | EBLCP |
| Modifying agency | YDXCP |
| -- | DG1 |
| -- | DEBSZ |
| -- | OCLCQ |
| -- | OCLCA |
| -- | OCLCF |
| -- | OCLCQ |
| -- | DEBBG |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9781118603338 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 1118603338 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9781118603246 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 1118603249 |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBSZ |
| System control number | 39748044X |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBSZ |
| System control number | 431339252 |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBSZ |
| System control number | 449346781 |
| 029 1# - (OCLC) | |
| OCLC library identifier | NZ1 |
| System control number | 15916046 |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBBG |
| System control number | BV043395465 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)828298898 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA274.2 .M33 2011 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 519.2/2 |
| -- | 519.22 |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Mackevičius, Vigirdas. |
| 245 10 - TITLE STATEMENT | |
| Title | Introduction to stochastic analysis : |
| Remainder of title | integrals and differential equations / |
| Statement of responsibility, etc | Vigirdas Mackevičius. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | London : |
| Name of publisher, distributor, etc | Wiley, |
| Date of publication, distribution, etc | 2013. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (278 pages). |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | ISTE |
| 588 0# - | |
| -- | Print version record. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 500 ## - GENERAL NOTE | |
| General note | 14.4. Itô processes. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 526 ## - STUDY PROGRAM INFORMATION NOTE | |
| Department | Life Sciences |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Stochastic analysis. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Stochastic analysis. |
| Source of heading or term | fast |
| -- | (OCoLC)fst01133499 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| Main entry heading | Mackevicius, Vigirdas. |
| Title | Introduction to Stochastic Analysis : Integrals and Differential Equations. |
| Place, publisher, and date of publication | London : Wiley, ©2013 |
| International Standard Book Number | 9781848213111 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | ISTE. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="http://dx.doi.org/10.1002/9781118603338">http://dx.doi.org/10.1002/9781118603338</a> |
| Public note | Wiley Online Library |
| 994 ## - | |
| -- | 92 |
| -- | DG1 |
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