Doubly Stochastic Poisson Processes

absolutely continuous absolutely dominated Assume B{dx best estimate best linear estimate Billingsley 1968 Borel algebra Borel measures bounded sets calculations Consider constant curve represents continuous curve represents defined definition denote distribution function doubly stochastic Poisson epochs of events equation example exists Figure finite follows from theorem function f g(eix given Grandell Hilbert space Illustration of estimates independent integrable intensity Kallenberg Kerstan Lebesgue measure lemma M{dx Matthes and Mecke non-atomic nonnegative notations o-algebra observed Palm probabilities piecewise constant curve piecewise continuous curve point process probability measure probability space proof of theorem random measure random variable renewal process Rudemo section 1.6 section A3 spectral density spike train represents stochastic Poisson process stochastic Poisson sequence stochastic process tion topology vague topology values vector weighted Poisson process zero