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Blackwell's renewal theorem for certain linear submartingales and coupling

Blackwell's renewal theorem for certain linear submartingales and coupling The present work surveys some extensions of Blackwell's renewal theorem for a certain class of linear submartingalesS ℕ which have been recently obtained by the author. The basic assumption onS ℕ is that their conditional increment distribution functions with respect to some filtration $$\mathcal{F}_\mathbb{N} $$ are bounded from above and below by integrable distribution functions. Under a further mean stability condition these random walks turn out to be natural candidates for satisfying Blackwell-type renewal theorems. The latter are derived by employing a coupling argument similar to that which has been used in the i.i.d. case by Lindvallet al. A number of applications are also presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Blackwell's renewal theorem for certain linear submartingales and coupling

Acta Applicandae Mathematicae , Volume 34 (2) – Dec 31, 2004

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References (19)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00994262
Publisher site
See Article on Publisher Site

Abstract

The present work surveys some extensions of Blackwell's renewal theorem for a certain class of linear submartingalesS ℕ which have been recently obtained by the author. The basic assumption onS ℕ is that their conditional increment distribution functions with respect to some filtration $$\mathcal{F}_\mathbb{N} $$ are bounded from above and below by integrable distribution functions. Under a further mean stability condition these random walks turn out to be natural candidates for satisfying Blackwell-type renewal theorems. The latter are derived by employing a coupling argument similar to that which has been used in the i.i.d. case by Lindvallet al. A number of applications are also presented.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 31, 2004

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