Zobrazeno 1 - 10
of 149
pro vyhledávání: '"Rolski, Tomasz"'
We consider a family of sup-functionals of (drifted) fractional Brownian motion with Hurst parameter $H\in(0,1)$. This family includes, but is not limited to: expected value of the supremum, expected workload, Wills functional, and Piterbarg-Pickands
Externí odkaz:
http://arxiv.org/abs/2110.08788
We derive the exact asymptotics of \[ P\left( \sup_{t\ge 0} \Bigl( X_1(t) - \mu_1 t\Bigr)> u, \ \sup_{s\ge 0} \Bigl( X_2(s) - \mu_2 s\Bigr)> u \right), \ \ u\to\infty, \] where $(X_1(t),X_2(s))_{t,s\ge0}$ is a correlated two-dimensional Brownian moti
Externí odkaz:
http://arxiv.org/abs/2003.02954
Publikováno v:
Risks 2019, 7(3), 83
We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function $P(u)$ for the component-wise ruin (that is both business lines
Externí odkaz:
http://arxiv.org/abs/1906.09347
A level-dependent L\'evy process solves the stochastic differential equation $dU(t) = dX(t)-{\phi}(U(t)) dt$, where $X$ is a spectrally negative L\'evy process. A special case is a multi-refracted L\'evy process with $\phi_k(x)=\sum_{j=1}^k\delta_j1_
Externí odkaz:
http://arxiv.org/abs/1712.00050
We analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions when the initial reserves of both companies tend to infini
Externí odkaz:
http://arxiv.org/abs/1702.01312
This paper derives an exact asymptotic expression for \[ \mathbb{P}_{\mathbf{x}_u}\{\exists_{t\ge0} \mathbf{X}(t)- \boldsymbol{\mu}t\in \mathcal{U} \}, \ \ {\rm as}\ \ u\to\infty, \] where $\mathbf{X}(t)=(X_1(t),\ldots,X_d(t))^\top,t\ge0$ is a correl
Externí odkaz:
http://arxiv.org/abs/1610.09387
Publikováno v:
In Stochastic Processes and their Applications December 2019 129(12):5406-5449
In this paper we analyze the quasi-stationary workload of a L\'evy-driven storage system. More precisely, assuming the system is in stationarity, we study its behavior conditional on the event that the busy period $T$ in which time 0 is contained has
Externí odkaz:
http://arxiv.org/abs/1012.2664
Publikováno v:
Stochastic Processes and their Applications 120 (2010) 2289-2301
This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish the asympt
Externí odkaz:
http://arxiv.org/abs/1006.0029
Many processes must complete in the presence of failures. Different systems respond to task failure in different ways. The system may resume a failed task from the failure point (or a saved checkpoint shortly before the failure point), it may give up
Externí odkaz:
http://arxiv.org/abs/0706.0403