Probability, Random Processes, and Statistical Analysis: Applications to Communications, Signal Processing, Queueing Theory and Mathematical FinanceTogether with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals. |
Contents
| 1 | |
Part I Probability random variables and statistics | 15 |
Part II Transform methods bounds and limits | 183 |
Part III Random processes | 313 |
Part IV Statistical inference | 521 |
Part V Applications and advanced topics | 571 |
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Common terms and phrases
algorithm analysis applied assume Bayesian Bernoulli Bernoulli trials binomial distribution Brownian motion called Chapter Cited coefficient complex-valued compute Consider continuous RV continuous-time convergence covariance CTMC defined denoted Derive discrete RV discrete-time discussed in Section distribution function DTMC equation equivalent ergodic Erlang estimate event Example exponential distribution exponential family Figure filter finite formula Fx(x Gaussian process given independent inequality integral interval large numbers likelihood function linear Markov chain Markov process mathematician matrix method node noise normal distribution observation obtain output Poisson distribution Poisson process probability distribution Problem queue random process random variable random walk recursion sample sequence server Show signal stationary distribution statistical stochastic theorem theory transform transition vector Viterbi algorithm Y₁ zero