On a.s. and r-mean convergence of random processes with an application to first passage times

DOI10.1007/BF00532871zbMath0291.60024MaRDI QIDQ4042410

Allan Gut

Publication date: 1975

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Stopping times; optimal stopping problems; gambling theory (60G40) Markov processes (60J99) Renewal theory (60K05)

Related Items (7)

On capital allocation for a risk measure derived from ruin theory ⋮ Stopped two-dimensional perturbed random walks and Lévy processes ⋮ On the moments of some first passage times and the associated processes ⋮ General optimal stopping with linear cost ⋮ Stopped Lévy processes with applications to first passage times ⋮ Generalized parking problems for levy processes ⋮ On efficient stopping times

Cites Work

• On the moments and limit distributions of some first passage times
• On convergence in r-mean of some first passage times and randomly indexed partial sums
• On the asymptotic distribution of the sum of a random number of independent random variables
• On a Stopping Rule and the Central Limit Theorem
• On Convergence in $r$-Mean of Normalized Partial Sums
• An $L^p$-Convergence Theorem
• Some One-Sided Stopping Rules
• On Wald's equations in continuous time
• On the $L_p$-Convergence for $n^{-1/p} S_n, 0 < p < 2^1$
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