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math.PR2026
On Lorden's Inequality and Renewal-Type Processes with Dependent Inter-renewal Times
El'mira Yu. Kalimulina, Galina A. Zverkina
We consider renewal-type processes whose positive inter-renewal times may be dependent, non-identically distributed, and may have mixed distributions. We introduce a generalised in…
math.PR2026
Uniform Lorden-type bounds for overshoot moments for standard exponential families: small drift and an exponential correction
El'mira Yu. Kalimulina, Mark Ya. Kelbert
We study the overshoot \(R_b=S_{Ï(b)}-b\) of a random walk with independent identically distributed increments from a standardised one-parameter exponential family, with primary e…