000			05178cam a2200553Mi 4500
001			ocn828298898
003			OCoLC
005			20171107093446.0
006			m o d
007			cr cnu|||unuuu
008			130223s2013 enk o 000 0 eng d
020			_a9781118603338 _q(electronic bk.)
020			_a1118603338 _q(electronic bk.)
020			_z9781118603246
020			_z1118603249
029	1		_aDEBSZ _b39748044X
029	1		_aDEBSZ _b431339252
029	1		_aDEBSZ _b449346781
029	1		_aNZ1 _b15916046
029	1		_aDEBBG _bBV043395465
035			_a(OCoLC)828298898
040			_aEBLCP _beng _epn _cEBLCP _dYDXCP _dDG1 _dDEBSZ _dOCLCQ _dOCLCA _dOCLCF _dOCLCQ _dDEBBG
049			_aMAIN
050		4	_aQA274.2 .M33 2011
082	0	4	_a519.2/2 _a519.22
100	1		_aMackevičius, Vigirdas.
245	1	0	_aIntroduction to stochastic analysis : integrals and differential equations / _cVigirdas Mackevičius. _h[electronic resource]
260			_aLondon : _bWiley, _c2013.
300			_a1 online resource (278 pages).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aISTE
500			_a14.4. Itô processes.
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.
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.
588	0		_aPrint version record.
650		0	_aStochastic analysis.
650		7	_aStochastic analysis. _2fast _0(OCoLC)fst01133499
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://onlinelibrary.wiley.com/book/10.1002/9781118603338 _zWiley Online Library
942			_2ddc _cBK
999			_c206471 _d206471