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General Introduction l
SecondOrder Random Functions
Stationary SecondOrder Processes
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a-field Af(x apply assume Borel boundary condition bounded Brownian motion cess Chapter Clearly compact construct convergence Corollary covariance function cylinder sets defined denote density differential equation e"Xt easy example exists exponential f G C(S fact Feller finite finite-dimensional distributions follows func function f Hence holds implies increments independent initial integral isometry Kolmogorov's large numbers Lebesgue measure lemma limit linear Markov chain Markov process Markov property Markov transition function martingale mathematics means measurable with respect measure dF metric space norm normal Markov process operator orthogonal orthonormal paths Poisson process probability space Problem Proof Proposition prove random process random variables result right-continuous satisfies semigroup sequence solution spectral measure spectral representation state-space stationary process stochastic matrix stochastic process stopping submartingale subset subspace Suppose theory tion uniformly unique unitary upcrossings vector verify Wiener process