## Technical Report, Issue 58 |

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### Contents

RECURRENT EVENTS LADDER PROCESSES IN DISCRETE | 6 |

LADDER REGENERATIVE EVENTS | 35 |

STRICT LADDER EPOCHS AND SOME FUNCTIONALS | 65 |

1 other sections not shown

### Common terms and phrases

absolutely continuous ascending ladder epochs assume bounded variation canonical measure chapter completes the proof compound Poisson process concept of ladder continuous time analogue converges dam process degenerate descending ladder event Doob l0 e"et er(e event S defined Feller Fj(x following theorem follows from Theorem function p(t Gaussian process given Hence identically distributed random independent identically distributed jumps Kingman ladder regenerative event Laplace transform last theorem Let X(t lim p(t M/G/l system Markov chains Markov property obtain occur infinitely p-function P{dx positive Pr{T probability process with stationary proof is complete queueing system queueing theory random walk recurrent event renewal process renewal sequence renewal theory sample function behavior Security Classification stable regenerative event standard and stable standard regenerative event stationary independent increments stochastic process strict ladder epochs sup X(t sup{t supremum Theorem 2.l4 theorem now follows x}dt Xj(t