Some Ladder Processes in Continuous Time with Application to Queues |
Common terms and phrases
ascending ladder heights basic identity behavior of N(t central limit theorem Chapter compound Poisson process convergent CORN CORNELL CORNELL LIBRARY CORNELL CORNELL UNIVERSITY CORNELL LIBRARY LIBRARY CORNELL UNIVERSITY CORNELL descending ladder epochs distributed random variables distribution F distribution of T₁ domain of attraction downward jumps equation fluctuation theory following theorem function identically distributed random independent and identically inf{t integers joint distribution ladder processes Laplace transform Lemma Let X(t LIBRARY CORNELL CORNELL LIBRARY LIBRARY CORNELL lim Pr{N(t limiting behavior limiting distribution Liouville's theorem Markov Property normal distribution normalizing sequences passage probability process defined random walk regions of convergence renewal quantities renewal sequence result sequence of ascending slowly varying stable law stationary and independent supremum T₁ t₂ unique root unit circle UNIVERSITY CORNELL CORNELL UNIVERSITY LIBRARY LIBRARY UNIVERSITY UNIVERSITY upward jumps varying at infinity write X(T₁ Z₁ Z₂ zero ZN(t