4 citations · 8 across the 7 of their papers we have counts for
7 papers · 1 filter
Weighted-threshold Coupon Collection
Sebastian Müller, Stjepan Šebek
We study a weighted-threshold version of the coupon collector problem in continuous time. Each type is discovered at rate and, once discovered, contributes weight ,…
On the convex hull of a planar Brownian bridge with a random Gaussian endpoint
Nikola Sandrić, Stjepan Šebek, Luka Šimek
We consider a one-parameter family of isotropic planar Gaussian processes \[ X_σ(t) =B_t+σt Z,\qquad 0\le t\le 1,\quad 0\le σ\le 1, \] where is a standard (-to-) planar B…
Expected perimeter and area of the convex hull of planar Brownian motion stopped upon exiting the unit disk
Rudi Mrazović, Hugo Panzo, Stjepan Šebek
We study the convex hull of planar Brownian motion run until the exit time from the unit disk. Our primary objectives are to compute the expected perimeter and expected area of thi…
Convex hull of Brownian motion and Brownian bridge
Stjepan Šebek
In this article we study the convex hull spanned by the union of trajectories of a standard planar Brownian motion, and an independent standard planar Brownian bridge. We find exac…
Convex hulls of stable random walks
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek
We consider convex hulls of random walks whose steps belong to the domain of attraction of a stable law in . We prove convergence of the convex hull in the space of a…
Limit theorems for a stable sausage
Wojciech Cygan, Nikola Sandrić, Stjepan Šebek
In this article, we study fluctuations of the volume of a stable sausage defined via a -dimensional rotationally invariant -stable process. As the main results, we establish…