Eckhard Schlemm

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The class of multivariate Lévy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of continuous-time state space models. The linear innovations of the weak ARMA process arising from sampling an MCARMA process at an equidistant grid are proved to(More)
We consider the parametric estimation of the driving Lévy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid (0, h, 2h, . . .). Beginning with a new state space representation, we develop a method to recover the driving Lévy process exactly from a continuous record of the(More)
We derive the distribution of the eigenvalues of a large sample covariance matrix when the data is dependent in time. More precisely, the dependence for each variable i = 1, . . . , p is modelled as a linear process (Xi,t)t=1,...,n = ( ∑∞ j=0 cjZi,t−j)t=1,...,n, where {Zi,t} are assumed to be independent random variables with finite fourth moments. If the(More)
In this work we consider two first-passage percolation problems. In the first part we concern ourselves with effectively one-dimensional graphs with vertex set {1 . . . , n}×{0, 1} and translation-invariant edge-structure. For three of six non-trivial cases we obtain exact expressions for the asymptotic percolation rate χ by solving certain recursive(More)
BACKGROUND AND PURPOSE Patients with acute ischemic stroke (AIS) and large vessel occlusion may benefit from direct transportation to an endovascular capable comprehensive stroke center (mothership approach) as opposed to direct transportation to the nearest stroke unit without endovascular therapy (drip and ship approach). The optimal transport strategy(More)
We consider the first-passage percolation problem on effectively one-dimensional graphs with vertex set {1 . . . , n} × {0, 1} and translation-invariant edge-structure. For three of six non-trivial cases we obtain exact expressions for the asymptotic percolation rate χ by solving certain recursive distributional equations and invoking results from ergodic(More)
We introduce a random matrix model where the entries are dependent across both rows and columns. More precisely, we investigate matrices of the form X = (X(i−1)n+t)it ∈ Rp×n derived from a linear process Xt = ∑ j c jZt− j, where the {Zt} are independent with bounded fourth moment. We show that, when both p and n tend to infinity such that the ratio p/n(More)