Applied Probability and Stochastic Processes: In Engineering and Physical Sciences
This introduction to modern concepts of applied stochastic processes is written for a broad range of applications in diverse areas of engineering and the physical sciences (unlike other books, which are written primarily for communications or electrical engineering). Emphasis is on clarifying the basic principles supporting current prediction techniques. The first eight chapters present the probability theory relevant to analysis of stochastic processes. The following nine chapters discuss principles, advanced techniques (including the procedures of spectral analysis and the development of the probability density function) and applications. Also features material found in the recent literature such as higher-order spectral analysis, the joint probability distribution of amplitudes and periods and non-Gaussian random processes. Includes numerous illustrative examples.
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Random Variables and Their Probability Distributions
Moments of Random Variables
Moment Generating Function Characteristic Function
9 other sections not shown
amplitude analysis applying assume asymptotic autocorrelation function average becomes called Chapter characteristic function conditional consider constant continuous cumulative distribution function defined Definition denoted derived discrete discussed domain equal equation estimator evaluated event Example exist expected expressed extreme value formula Fourier transform frequency function is given given in Eq Hence impulse input integration interval joint probability density let us consider linear system maxima mean and variance mean value method negative nonlinear normal distribution noted observed obtained occurrence output parameter period Poisson distribution Poisson process positive presented probability density function probability distribution problem Proof properties proved random variable relationship renewal represents respectively sample space satisfies shown in Figure shows solution spectral density function spectrum statistically statistically independent stochastic process taking Theorem tion Type unit variable X wave write written zero