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SC505 STOCHASTIC PROCESSES Class Notes

SC505 STOCHASTICPROCESSESC lassNotesc Casta~non & Electricaland ComputerEngineeringBostonUniversityColle geof Engineering8 St. Mary'sStreetBoston,MA02215 Fall 20042 Contents1 Introductionto Probability .. andIndependenceof Events.. RandomVariables.. RandomVariables.. RandomVariables.. ,Densities,andExpectations.. theCovarianceMatrix.. inequality.. Inequality .. 'sInequality .. Inequalities..372 Sequencesof .. of LargeNumbers.. Convergence.. theLaw of LargeNumbersandtheCentralLimitTheorem.. RandomVariables..523 .. StochasticProcesses.. of StochasticProcesses.. StochasticProcesses.. StochasticProcesses.. RandomProcesses.. :Phase-ShiftKeying.. Functionsof VectorProcesses.. of Wide-senseStationaryProcesses.. SpectralDensity of Wide-SenseStationaryProcesses..714 of StochasticProcesses.. erentiation.. erentiationof GaussianStochasticProcesses.. of StationaryRandomProcesses.

repeated experiments. Note the emphases in the above de nition. The basis of probabilistic analysis is to determine or estimate the probabilities that certain known events occur, and then to use the axioms of probability theory to combine this information to derive probabilities of other events of interest, and to

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