Doubly Stochastic Poisson Processes

absolutely continuous absolutely dominated Assume assumptions asymptotically B(X)-measurable B{dx best estimate best linear estimate Billingsley 1968 Borel algebra Borel measures bounded sets calculations Consider constant curve represents continuous curve represents convergence defined definition denote distribution function doubly stochastic Poisson epochs of events equation example exists finite follows from theorem function f g(eix given Grandell Hilbert space Illustration of estimates independent integrable Jagers Kallenberg Kerstan Lebesgue measure lemma M{dx Markov chain Matthes and Mecke N{dx non-atomic nonnegative notations o-algebra observed Palm probabilities piecewise constant curve piecewise continuous curve point process probability measure probability space random measure random variable Rudemo sample functions section 1.6 simple point processes spike train represents stochastic Poisson process stochastic Poisson sequence stochastic process tion topology values vector weighted Poisson process zero हु