Random Walks With Stochastically Bounded Increments: Foundations and Characterization Results
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We consider random walks Sℕ, adapted to a filtration \(\cal F_N\), whose conditional increment distribution functions are bounded from above and/or below by an integrable distribution function. A further stability condition on the conditional increment means is also introduced. Such random walks share a number of properties with those having i.i.d. increments, in particular a uniform law of large numbers. In this paper, which is accompanied by a second one on renewal theory, we derive their basic properties and give equivalent characterizations in terms of certain drift constants which are introduced before and of great importance for a renewal theoretic analysis.
KeywordsRandom Walk Canonical Representation Entrance Time Renewal Theory Maximal Minorant
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