000			06860cam a2200745Ia 4500
001			ocn268966013
003			OCoLC
005			20240925133126.0
006			m d
007			cr cnu---unuuu
008			081105s2001 si ob 001 0 eng d
040			_aN$T _beng _epn _cN$T _dOCLCQ _dUBY _dIDEBK _dE7B _dOCLCQ _dOCLCF _dDKDLA _dOCLCQ _dNLGGC _dOCLCO _dYDXCP _dEBLCP _dDEBSZ _dOCLCO _dOCLCQ _dOCLCO
019			_a505144461 _a646769031 _a764502850 _a879074242
020			_a9789812810540 _q(electronic bk.)
020			_a9812810544 _q(electronic bk.)
020			_z9789810243852
020			_z9810243855 _q(alk. paper)
035			_a(OCoLC)268966013 _z(OCoLC)505144461 _z(OCoLC)646769031 _z(OCoLC)764502850 _z(OCoLC)879074242
050		4	_aTA342 _b.M35 2001eb
072		7	_aTEC _x009000 _2bisacsh
072		7	_aTEC _x035000 _2bisacsh
082	0	4	_a620/.001/5118 _222
049			_aMAIN
100	1		_aMamontov, Yevgeny, _d1955- _9434859
245	1	0	_aHigh-dimensional nonlinear diffusion stochastic processes _h[electronic resource] : _bmodelling for engineering applications / _cYevgeny Mamontov, Magnus Willander.
260			_aSingapore ; _aRiver Edge, NJ : _bWorld Scientific, _c2001.
300			_a1 online resource (xviii, 297 pages).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aSeries on advances in mathematics for applied sciences ; _vv. 56
504			_aIncludes bibliographical references (and index.
588	0		_aPrint version record.
520	8		_aAnnotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations. The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided.
505	0		_aPreface; Contents; Chapter 1 Introductory Chapter; 1.1 Prerequisites for Reading; 1.2 Random Variable. Stochastic Process. Random Field. High-Dimensional Process. One-Point Process; 1.3 Two-Point Process. Expectation. Markov Process. Example of Non-Markov Process Associated with Multidimensional Markov Process; 1.4 Preceding Subsequent and Transition Probability Densities. The Chapman-Kolmogorov Equation. Initial Condition for Markov Process; 1.4.1 The Chapman-Kolmogorov equation; 1.4.2 Initial condition for Markov process.
505	8		_a1.5 Homogeneous Markov Process. Example of Markov Process: The Wiener Process1.6 Expectation Variance and Standard Deviations of Markov Process; 1.7 Invariant and Stationary Markov Processes. Covariance. Spectral Densities; 1.8 Diffusion Process; 1.9 Example of Diffusion Processes: Solutions of Ito's Stochastic Ordinary Differential Equation; 1.10 The Kolmogorov Backward Equation; 1.11 Figures of Merit. Diffusion Modelling of High-Dimensional Systems; 1.12 Common Analytical Techniques to Determine Probability Densities of Diffusion Processes. The Kolmogorov Forward Equation.
505	8		_a1.12.1 Probability density1.12.2 Invariant probability density; 1.12.3 Stationary probability density; 1.13 The Purpose and Content of This Book; Chapter 2 Diffusion Processes; 2.1 Introduction; 2.2 Time-Derivatives of Expectation and Variance; 2.3 Ordinary Differential Equation Systems for Expectation; 2.3.1 The first-order system; 2.3.2 The second-order system; 2.3.3 Systems of the higher orders; 2.4 Models for Noise-Induced Phenomena in Expectation; 2.4.1 The case of stochastic resonance; 2.4.2 Practically efficient implementation of the second-order system.
505	8		_a2.5 Ordinary Differential Equation System for Variance2.5.1 Damping matrix; 2.5.2 The uncorrelated-matrixes approximation; 2.5.3 Nonlinearity of the drift function; 2.5.4 Fundamental limitation of the state-space-independent approximations for the diffusion and damping matrixes; 2.6 The Steady-State Approximation for The Probability Density; Chapter 3 Invariant Diffusion Processes; 3.1 Introduction; 3.2 Preliminary Remarks; 3.3 Expectation. The Finite-Equation Method; 3.4 Explicit Expression for Variance; 3.5 The Simplified Detailed-Balance Approximation for Invariant Probability Density.
505	8		_a3.5.1 Partial differential equation for logarithm of the density3.5.2 Truncated equation for the logarithm and the detailed-balance equation; 3.5.3 Case of the detailed balance; 3.5.4 The detailed-balance approximation; 3.5.5 The simplified detailed-balance approximation. Theorem on the approximating density; 3.6 Analytical-Numerical Approach to Non-Invariant and Invariant Diffusion Processes; 3.6.1 Choice of the bounded domain of the integration; 3.6.2 Evaluation of the multifold integrals. The Monte Carlo technique; 3.6.3 Summary of the approach; 3.7 Discussion.
650		0	_aEngineering _xMathematical models. _945759
650		0	_aStochastic processes. _91109
650		0	_aDiffusion processes. _970248
650		0	_aDifferential equations, Nonlinear. _95321
650		6	_aIngénierie _xModèles mathématiques. _9434860
650		6	_aProcessus stochastiques. _911127
650		6	_aProcessus de diffusion.
650		6	_aÉquations différentielles non linéaires. _911406
650		7	_aTECHNOLOGY & ENGINEERING _xEngineering (General) _2bisacsh _927299
650		7	_aTECHNOLOGY & ENGINEERING _xReference. _2bisacsh _927300
650		7	_aDifferential equations, Nonlinear. _2fast _0(OCoLC)fst00893474 _95321
650		7	_aDiffusion processes. _2fast _0(OCoLC)fst00893561 _970248
650		7	_aEngineering _xMathematical models. _2fast _0(OCoLC)fst00910373 _945759
650		7	_aStochastic processes. _2fast _0(OCoLC)fst01133519 _91109
655		4	_aElectronic books. _9396
655		0	_aElectronic books. _9396
700	1		_aWillander, M. _9115955
776	0	8	_iPrint version: _aMamontov, Yevgeny, 1955- _tHigh-dimensional nonlinear diffusion stochastic processes. _dSingapore ; River Edge, NJ : World Scientific, 2001 _z9810243855 _z9789810243852 _w(DLC) 00053437 _w(OCoLC)45283225
830		0	_aSeries on advances in mathematics for applied sciences ; _vv. 56. _9386502
856	4	0	_3EBSCOhost _uhttps://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235902
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938			_aEBSCOhost _bEBSC _n235902
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994			_a92 _bN$T
999			_c701881 _d701881