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040 MiAaPQ|beng|erda|epn|cMiAaPQ|dMiAaPQ
050 4 TK5102.5.P6725 2004
082 0 621.382
100 1 Primak, Serguei
245 10 Stochastic Methods and Their Applications to
Communications :|bStochastic Differential Equations
Approach
250 1st ed
264 1 Hoboken :|bJohn Wiley & Sons, Incorporated,|c2004
264 4 |c©2005
300 1 online resource (448 pages)
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
505 0 Stochastic Methods and Their Applications to
Communications -- Contents -- 1. Introduction -- 1.1
Preface -- 1.2 Digital Communication Systems -- 2. Random
Variables and Their Description -- 2.1 Random Variables
and Their Description -- 2.1.1 Definitions and Method of
Description -- 2.1.1.1 Classification -- 2.1.1.2
Cumulative Distribution Function -- 2.1.1.3 Probability
Density Function -- 2.1.1.4 The Characteristic Function
and the Log-Characteristic Function -- 2.1.1.5 Statistical
Averages -- 2.1.1.6 Moments -- 2.1.1.7 Central Moments --
2.1.1.8 Other Quantities -- 2.1.1.9 Moment and Cumulant
Generating Functions -- 2.1.1.10 Cumulants -- 2.2
Orthogonal Expansions of Probability Densities: Edgeworth
and Laguerre Series -- 2.2.1 The Edgeworth Series -- 2.2.2
The Laguerre Series -- 2.2.3 Gram-Charlier Series -- 2.3
Transformation of Random Variables -- 2.3.1 Transformation
of a Given PDF into an Arbitrary PDF -- 2.3.2 PDF of a
Harmonic Signal with Random Phase -- 2.4 Random Vectors
and Their Description -- 2.4.1 CDF, PDF and the
Characteristic Function -- 2.4.2 Conditional PDF -- 2.4.3
Numerical Characteristics of a Random Vector -- 2.5
Gaussian Random Vectors -- 2.6 Transformation of Random
Vectors -- 2.6.1 PDF of a Sum, Difference, Product and
Ratio of Two Random Variables -- 2.6.2 Probability Density
of the Magnitude and the Phase of a Complex Random Vector
with Jointly Gaussian Components -- 2.6.2.1 Zero Mean
Uncorrelated Gaussian Components of Equal Variance --
2.6.2.2 Case of Uncorrelated Components with Equal
Variances and Non-Zero Mean -- 2.6.3 PDF of the Maximum
(Minimum) of two Random Variables -- 2.6.4 PDF of the
Maximum (Minimum) of n Independent Random Variables -- 2.7
Additional Properties of Cumulants -- 2.7.1 Moment and
Cumulant Brackets -- 2.7.2 Properties of Cumulant Brackets
-- 2.7.3 More on the Statistical Meaning of Cumulants
505 8 2.8 Cumulant Equations -- 2.8.1 Non-Linear Transformation
of a Random Variable: Cumulant Method -- Appendix:
Cumulant Brackets and Their Calculations -- 3. Random
Processes -- 3.1 General Remarks -- 3.2 Probability
Density Function (PDF) -- 3.3 The Characteristic Functions
and Cumulative Distribution Function -- 3.4 Moment
Functions and Correlation Functions -- 3.5 Stationary and
Non-Stationary Processes -- 3.6 Covariance Functions and
Their Properties -- 3.7 Correlation Coefficient -- 3.8
Cumulant Functions -- 3.9 Ergodicity -- 3.10 Power
Spectral Density (PSD) -- 3.11 Mutual PSD -- 3.11.1 PSD of
a Sum of Two Stationary and Stationary Related Random
Processes -- 3.11.2 PSD of a Product of Two Stationary
Uncorrelated Processes -- 3.12 Covariance Function of a
Periodic Random Process -- 3.12.1 Harmonic Signal with a
Constant Magnitude -- 3.12.2 A Mixture of Harmonic Signals
-- 3.12.3 Harmonic Signal with Random Magnitude and Phase
-- 3.13 Frequently Used Covariance Functions -- 3.14
Normal (Gaussian) Random Processes -- 3.15 White Gaussian
Noise (WGN) -- 4. Advanced Topics in Random Processes --
4.1 Continuity, Differentiability and Integrability of a
Random Process -- 4.1.1 Convergence and Continuity --
4.1.2 Differentiability -- 4.1.3 Integrability -- 4.2
Elements of System Theory -- 4.2.1 General Remarks --
4.2.2 Continuous SISO Systems -- 4.2.3 Discrete Linear
Systems -- 4.2.4 MIMO Systems -- 4.2.5 Description of Non-
Linear Systems -- 4.3 Zero Memory Non-Linear
Transformation of Random Processes -- 4.3.1 Transformation
of Moments and Cumulants -- 4.3.1.1 Direct Method --
4.3.1.2 The Rice Method -- 4.3.2 Cumulant Method -- 4.4
Cumulant Analysis of Non-Linear Transformation of Random
Processes -- 4.4.1 Cumulants of the Marginal PDF -- 4.4.2
Cumulant Method of Analysis of Non-Gaussian Random
Processes -- 4.5 Linear Transformation of Random Processes
505 8 4.5.1 General Expression for Moment and Cumulant Functions
at the Output of a Linear System -- 4.5.1.1 Transformation
of Moment and Cumulant Functions -- 4.5.1.2 Linear Time-
Invariant System Driven by a Stationary Process -- 4.5.2
Analysis of Linear MIMO Systems -- 4.5.3 Cumulant Method
of Analysis of Linear Transformations -- 4.5.4
Normalization of the Output Process by a Linear System --
4.6 Outages of Random Processes -- 4.6.1 General
Considerations -- 4.6.2 Average Level Crossing Rate and
the Average Duration of the Upward Excursions -- 4.6.3
Level Crossing Rate of a Gaussian Random Process -- 4.6.4
Level Crossing Rate of the Nakagami Process -- 4.6.5
Concluding Remarks -- 4.7 Narrow Band Random Processes --
4.7.1 Definition of the Envelope and Phase of Narrow Band
Processes -- 4.7.2 The Envelope and the Phase
Characteristics -- 4.7.2.1 Blanc-Lapierre Transformation -
- 4.7.2.2 Kluyver Equation -- 4.7.2.3 Relations Between
Moments of p(A(n)) (a(n)) and p(i)(I) -- 4.7.2.4 The Gram-
Charlier Series for p(xR) (x) and p(i)(I) -- 4.7.3
Gaussian Narrow Band Process -- 4.7.3.1 First Order
Statistics -- 4.7.3.2 Correlation Function of the In-phase
and Quadrature Components -- 4.7.3.3 Second Order
Statistics of the Envelope -- 4.7.3.4 Level Crossing Rate
-- 4.7.4 Examples of Non-Gaussian Narrow Band Random
Processes -- 4.7.4.1 K Distribution -- 4.7.4.2 Gamma
Distribution -- 4.7.4.3 Log-Normal Distribution -- 4.7.4.4
A Narrow Band Process with Nakagami Distributed Envelope -
- 4.8 Spherically Invariant Processes -- 4.8.1 Definitions
-- 4.8.2 Properties -- 4.8.2.1 Joint PDF of a SIRV --
4.8.2.2 Narrow Band SIRVs -- 4.8.3 Examples -- 5. Markov
Processes and Their Description -- 5.1 Definitions --
5.1.1 Markov Chains -- 5.1.2 Markov Sequences -- 5.1.3 A
Discrete Markov Process -- 5.1.4 Continuous Markov
Processes
505 8 5.1.5 Differential Form of the Kolmogorov-Chapman Equation
-- 5.2 Some Important Markov Random Processes -- 5.2.1 One
-Dimensional Random Walk -- 5.2.1.1 Unrestricted Random
Walk -- 5.2.2 Markov Processes with Jumps -- 5.2.2.1 The
Poisson Process -- 5.2.2.2 A Birth Process -- 5.2.2.3 A
Death Process -- 5.2.2.4 A Death and Birth Process -- 5.3
The Fokker-Planck Equation -- 5.3.1 Preliminary Remarks --
5.3.2 Derivation of the Fokker-Planck Equation -- 5.3.3
Boundary Conditions -- 5.3.4 Discrete Model of a
Continuous Homogeneous Markov Process -- 5.3.5 On the
Forward and Backward Kolmogorov Equations -- 5.3.6 Methods
of Solution of the Fokker-Planck Equation -- 5.3.6.1
Method of Separation of Variables -- 5.3.6.2 The Laplace
Transform Method -- 5.3.6.3 Transformation to the
Schrödinger Equations -- 5.4 Stochastic Differential
Equations -- 5.4.1 Stochastic Integrals -- 5.5 Temporal
Symmetry of the Diffusion Markov Process -- 5.6 High Order
Spectra of Markov Diffusion Processes -- 5.7 Vector Markov
Processes -- 5.7.1 Definitions -- 5.7.1.1 A Gaussian
Process with a Rational Spectrum -- 5.8 On Properties of
Correlation Functions of One-Dimensional Markov Processes
-- 6. Markov Processes with Random Structures -- 6.1
Introduction -- 6.2 Markov Processes with Random Structure
and Their Statistical Description -- 6.2.1 Processes with
Random Structure and Their Classification -- 6.2.2
Statistical Description of Markov Processes with Random
Structure -- 6.2.3 Generalized Fokker-Planck Equation for
Random Processes with Random Structure and Distributed
Transitions -- 6.2.4 Moment and Cumulant Equations of a
Markov Process with Random Structure -- 6.3 Approximate
Solution of the Generalized Fokker-Planck Equations --
6.3.1 Gram-Charlier Series Expansion -- 6.3.1.1
Eigenfunction Expansion -- 6.3.1.2 Small Intensity
Approximation
505 8 6.3.1.3 Form of the Solution for Large Intensity -- 6.3.2
Solution by the Perturbation Method for the Case of Low
Intensities of Switching -- 6.3.2.1 General Small
Parameter Expansion of Eigenvalues and Eigenfunctions --
6.3.2.2 Perturbation of Y(0)(x) -- 6.3.3 High Intensity
Solution -- 6.3.3.1 Zero Average Current Condition --
6.3.3.2 Asymptotic Solution P(x) -- 6.3.3.3 Case of a
Finite Intensity v -- 6.4 Concluding Remarks -- 7.
Synthesis of Stochastic Differential Equations -- 7.1
Introduction -- 7.2 Modeling of a Scalar Random Process
Using a First Order SDE -- 7.2.1 General Synthesis
Procedure for the First Order SDE -- 7.2.2 Synthesis of an
SDE with PDF Defined on a Part of the Real Axis -- 7.2.3
Synthesis of l Processes -- 7.2.4 Non-Diffusion Markov
Models of Non-Gaussian Exponentially Correlated Processes
-- 7.2.4.1 Exponentially Correlated Markov Chain-DAR(1)
and Its Continuous Equivalent -- 7.2.4.2 A Mixed Process
with Exponential Correlation -- 7.3 Modeling of a One-
Dimensional Random Process on the Basis of a Vector SDE --
7.3.1 Preliminary Comments -- 7.3.2 Synthesis Procedure of
a (l, w) Process -- 7.3.3 Synthesis of a Narrow Band
Process Using a Second Order SDE -- 7.3.3.1 Synthesis of a
Narrow Band Random Process Using a Duffing Type SDE --
7.3.3.2 An SDE of the Van Der Pol Type -- 7.4 Synthesis of
a One-Dimensional Process with a Gaussian Marginal PDF and
Non-Exponential Correlation -- 7.5 Synthesis of Compound
Processes -- 7.5.1 Compound L Process -- 7.5.2 Synthesis
of a Compound Process with a Symmetrical PDF -- 7.6
Synthesis of Impulse Processes -- 7.6.1 Constant Magnitude
Excitation -- 7.6.2 Exponentially Distributed Excitation -
- 7.7 Synthesis of an SDE with Random Structure -- 8.
Applications -- 8.1 Continuous Communication Channels --
8.1.1 A Mathematical Model of a Mobile Satellite
Communication Channel
505 8 8.1.2 Modeling of a Single-Path Propagation
520 Stochastic Methods & their Applications to Communications
presents a valuable approach to the modelling, synthesis
and numerical simulation of random processes with
applications in communications and related fields. The
authors provide a detailed account of random processes
from an engineering point of view and illustrate the
concepts with examples taken from the communications area.
The discussions mainly focus on the analysis and synthesis
of Markov models of random processes as applied to
modelling such phenomena as interference and fading in
communications. Encompassing both theory and practice,
this original text provides a unified approach to the
analysis and generation of continuous, impulsive and mixed
random processes based on the Fokker-Planck equation for
Markov processes. Presents the cumulated analysis of
Markov processes Offers a SDE (Stochastic Differential
Equations) approach to the generation of random processes
with specified characteristics Includes the modelling of
communication channels and interfer ences using SDE
Features new results and techniques for the of solution of
the generalized Fokker-Planck equation Essential reading
for researchers, engineers, and graduate and upper year
undergraduate students in the field of communications,
signal processing, control, physics and other areas of
science, this reference will have wide ranging appeal
588 Description based on publisher supplied metadata and other
sources
590 Electronic reproduction. Ann Arbor, Michigan : ProQuest
Ebook Central, 2020. Available via World Wide Web. Access
may be limited to ProQuest Ebook Central affiliated
libraries
650 0 Telecommunication -- Mathematics.;Stochastic differential
equations
655 4 Electronic books
700 1 Lyandres, Vladimir
700 1 Kontorovich, Valeri
776 08 |iPrint version:|aPrimak, Serguei|tStochastic Methods and
Their Applications to Communications : Stochastic
Differential Equations Approach|dHoboken : John Wiley &
Sons, Incorporated,c2004|z9780470847411
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