8 citations · 9 across the 3 of their papers we have counts for
4 papers
Penalizing fractional Brownian motion for being negative
Frank Aurzada, Micha Buck, Martin Kilian
We study a modification of the fractional analogue of the Brownian meander, which is Brownian motion conditioned to be positive on the time interval . More precisely, we d…
Ruin probabilities in the Cramér-Lundberg model with temporarily negative capital
Frank Aurzada, Micha Buck
We study the asymptotics of the ruin probability in the Cramér-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the…
Limit theorems for random walks with absorption
Micha Buck
We introduce a class of absorption mechanisms and study the behavior of real-valued centered random walks with finite variance that do not get absorbed. In particular, we prove per…
Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences
Frank Aurzada, Micha Buck
We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brow…