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7 papers · 2 filters
Predicting the Last Zero of Brownian Motion with Drift
J. du Toit, G. Peskir, A. N. Shiryaev
Given a standard Brownian motion with drift and letting denote the last zero of before , we consider the optimal prediction probl…
A note on the supremum of a stable process
R. A. Doney
If is a spectrally positive stable process of index whose Lévy measure has density on and it is known that $P(S_…
Rapid paths in von Neumann-Gale dynamical systems
Wael Bahsoun, Igor V. Evstigneev, Michael I. Taksar
The paper examines random dynamical systems related to the classical von Neumann and Gale models of economic growth. Such systems are defined in terms of multivalued operators in s…
Curve crossing for random walks reflected at their maximum
Ron Doney, Ross Maller
Let be a random walk reflected in its maximum. Except in the trivial case when , will pass over a horizontal boundary of a…
The law of the supremum of a stable Lévy process with no negative jumps
Violetta Bernyk, Robert C. Dalang, Goran Peskir
Let be a stable Lévy process of index with no negative jumps and let denote its running supremum for . We show that t…
The trap of complacency in predicting the maximum
J. du Toit, G. Peskir
Given a standard Brownian motion with drift and letting for , we consider the optimal pre…