K. Kosiński

activity

20102016

most citedOn the infimum attained by the reflected fractional Brownian motion

28 citations · 41 across the 4 of their papers we have counts for

collaborators

9 papers

math.PR2016★ 3 cited

An Erdös-Révész type law of the iterated logarithm for reflected fractional Brownian motion

K. Dębicki, K. M. Kosiński

Let $B_{H} = {B_{H} (t) : t \in R}$ be a fractional Brownian motion with Hurst parameter $H \in (0, 1)$ . For the stationary storage process $Q_{B_H}(t)=\sup_{-\infty<s\le t}(B_H(t)-B_H…

math.PR2016★ 4 cited

An Erdös--Révész type law of the iterated logarithm for order statistics of a stationary Gaussian process

K. Dębicki, K. M. Kosiński

Let ${X (t) : t \in R_{+}}$ be a stationary Gaussian process with almost surely (a.s.) continuous sample paths, $E X (t) = 0$ , $E X^{2} (t) = 1$ and correlation func…

math.PR2013★ 28 cited

On the infimum attained by the reflected fractional Brownian motion

Krzysztof Dębicki, Kamil Marcin Kosiński

Let ${B_{H} (t) : t \geq 0}$ be a fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2}, 1)$ . For the storage process $Q_{B_H}(t)=\sup_{-\infty\le s\le t} \left(B_H(t)-B_H(s)…

math.PR2012

Logarithmic asymptotics for multidimensional extremes under non-linear scalings

Kamil Marcin Kosinski, Michel Mandjes

Let $W = {W_{n} : n \in N}$ be a sequence of random vectors in $R^{d}$ , $d \geq 1$ . This paper considers the logarithmic asymptotics of the extremes o…

math.PR2011

Queue lengths and workloads in polling systems

Onno Boxma, Offer Kella, Kamil Marcin Kosinski

We consider a polling system: a queueing system of $N \geq 1$ queues with Poisson arrivals $Q_{1}, ..., Q_{N}$ visited in a cyclic order (with or without switchover times) by a single serv…

math.PR2011

Gaussian queues in light and heavy traffic

Krzysztof Debicki, Kamil Marcin Kosinski, Michel Mandjes

In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\equiv\{X(t):t\in…