| 000 | 05154cam a2200565Mi 4500 | ||
|---|---|---|---|
| 001 | ocn828298898 | ||
| 003 | OCoLC | ||
| 005 | 20230823095530.0 | ||
| 006 | m o d | ||
| 007 | cr cnu|||unuuu | ||
| 008 | 130223s2013 enk o 000 0 eng d | ||
| 040 |
_aEBLCP _beng _epn _cEBLCP _dYDXCP _dDG1 _dDEBSZ _dOCLCQ _dOCLCA _dOCLCF _dOCLCQ _dDEBBG |
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| 020 |
_a9781118603338 _q(electronic bk.) |
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| 020 |
_a1118603338 _q(electronic bk.) |
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| 020 | _z9781118603246 | ||
| 020 | _z1118603249 | ||
| 029 | 1 |
_aDEBSZ _b39748044X |
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| 029 | 1 |
_aDEBSZ _b431339252 |
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| 029 | 1 |
_aDEBSZ _b449346781 |
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| 029 | 1 |
_aNZ1 _b15916046 |
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| 029 | 1 |
_aDEBBG _bBV043395465 |
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| 035 | _a(OCoLC)828298898 | ||
| 050 | 4 | _aQA274.2 .M33 2011 | |
| 082 | 0 | 4 |
_a519.2/2 _a519.22 |
| 049 | _aMAIN | ||
| 100 | 1 | _aMackevičius, Vigirdas. | |
| 245 | 1 | 0 |
_aIntroduction to stochastic analysis : _bintegrals and differential equations / _cVigirdas Mackevičius. |
| 260 |
_aLondon : _bWiley, _c2013. |
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| 300 | _a1 online resource (278 pages). | ||
| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 490 | 1 | _aISTE | |
| 588 | 0 | _aPrint version record. | |
| 505 | 0 | _aCover; 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 | _aChapter 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 | _aChapter 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 | _a11.2. 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 | _aChapter 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 | _a14.4. Itô processes. | ||
| 520 | _aThis 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. | ||
| 650 | 0 | _aStochastic analysis. | |
| 650 | 7 |
_aStochastic analysis. _2fast _0(OCoLC)fst01133499 |
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| 655 | 4 | _aElectronic books. | |
| 776 | 0 | 8 |
_iPrint version: _aMackevicius, Vigirdas. _tIntroduction to Stochastic Analysis : Integrals and Differential Equations. _dLondon : Wiley, ©2013 _z9781848213111 |
| 830 | 0 | _aISTE. | |
| 856 | 4 | 0 |
_uhttp://dx.doi.org/10.1002/9781118603338 _zWiley Online Library |
| 994 |
_a92 _bDG1 |
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| 999 |
_c20177 _d20136 |
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| 526 | _bls | ||