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Conditioned limit theorems and heavy traffic. (English) Zbl 0535.60020

Summary: In this note we prove a generalisation of a conditioned functional central limit theorem of E. Bolthausen [cf. ibid. 4, 480-485 (1976; Zbl 0336.60024)]. This generalisation explains the nature of the discontinuity between such conditioned limit theorems for random walks (or in queueing for waiting times) with or without drift.

MSC:

60F05 Central limit and other weak theorems
60K25 Queueing theory (aspects of probability theory)
60J65 Brownian motion

Citations:

Zbl 0336.60024
Full Text: DOI