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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)

- Peter J. Brockwell, Eckhard Schlemm
- J. Multivariate Analysis
- 2013

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)

- Eckhard Schlemm
- 2012

We suggest a new method to compute the asymptotic fitness distribution in the Bak–Sneppen model of biological evolution. As applications we derive the full asymptotic distribution in the four-species model, and give an explicit linear recurrence relation for a set of coefficients determining the asymptotic distribution in the five-species model.

- Eckhard Schlemm
- 2008

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)

- ECKHARD SCHLEMM
- 2009

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)

- ECKHARD SCHLEMM
- 2010

We consider the first passage percolation problem on the random graph with vertex set N×{0, 1}, edges joining vertices at a Euclidean distance equal to unity, and independent exponential edgeweights. We provide a central limit theorem for the first passage times ln between the vertices (0, 0) and (n, 0), thus extending earlier results about the almost-sure… (More)

- ECKHARD SCHLEMM
- 2008

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)