Stochastic Processes; Lectures, 1972/73 |
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1817 LIBRARIES Af(x assume boundary condition bounded Brownian motion C₂ chapter CHIGAN Clearly conditional expectation consider convergence covariance function defined definition density differential equation easy ergodic example exists f dP f₁ F₂ fact Feller finite finite-dimensional distributions follows function f Hence Hilbert space holds implies increments independent integral L₂ L₂(dF large numbers lemma limit linear Markov chain Markov process Markov property Markov transition function martingale matrix metric MICHI MICHIGAN non-negative norm normal Markov process operator orthogonal paths probability space Problem proof Proposition prove Pt(x random process random variables result right-continuous satisfies semigroup sequence solution spectral measure stationary process stochastic matrix stochastic process stopping submartingale Suppose t₁ T₂ theorem theory transition function Pt uniformly unique UNIVE UNIVERSITY vector verify Wiener process X₁