## Stochastic methods and their applications to communications: stochastic differential equations approachStochastic 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. |

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### Contents

Introduction | 1 |

Random Variables and Their Description | 7 |

Random Processes | 59 |

Copyright | |

8 other sections not shown

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### Common terms and phrases

analysis applications approximation assumed average calculate characteristic function coefficients communication channel components considered correlation function correlation interval corresponding covariance function depend derivative described deterministic differential equation diffusion Markov process discrete distribution eigenvalues envelope equal to zero error example expansion expression fading channel filter finite Fokker-Planck equation Fourier transform frequency Gaussian process Gaussian random given higher order IEEE IEEE Trans impulse response initial conditions input process integral J-oo joint PDF Kontorovich level crossing rate linear system marginal PDF Markov chain Markov process matrix moments Nakagami narrow band process noise non-Gaussian obtained output process parameters phase polynomials possible probability density function process f process with random properties random process random structure random variable random vector Rayleigh Rayleigh fading rewritten second order sides of eq solution spectral density spectrum stationary process statistical Stochastic Differential Equations Stratonovich switching symmetric trajectory variance