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Approaching of Renewal Schemes

In: Coupling and Ergodic Theorems for Semi-Markov-Type Processes I

Author

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  • Dmitrii Silvestrov

    (Stockholm University, Department of Mathematics)

Abstract

In this chapter, we present the algorithm of approaching renewal points for two independent renewal schemes to a distance less than or equal to some H > 0 appearing as a result of alternating overjumps for renewal points of these renewal schemes. We define a renewal scheme, informally formulate and describe the coupling problem for renewal schemes, present the corresponding approaching renewal algorithm, and give explicit upper bounds for power and exponential moments of approaching times for renewal points using the method of test function. We also give explicit upper bounds for power and exponential moments of approaching times of renewal points uniform with respect to the initial distance between renewal points.

Suggested Citation

  • Dmitrii Silvestrov, 2025. "Approaching of Renewal Schemes," Springer Books, in: Coupling and Ergodic Theorems for Semi-Markov-Type Processes I, chapter 0, pages 229-278, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-89311-7_6
    DOI: 10.1007/978-3-031-89311-7_6
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