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Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes 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… (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 ∈ R p×n derived from a linear process X t = j c j Z t− j , where the {Z t } are independent with bounded fourth moment. We show that, when both p and n tend to infinity such that the ratio… (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 where {Z i,t } are assumed to be independent random variables with finite fourth moments. If the sample size n and the number of variables p = pn… (More)

- 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 per-colation rate χ by solving certain recursive… (More)

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

- 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
- 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)

- Eckhard Schlemm
- Mathematical biosciences
- 2015

The Bak-Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a… (More)

We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-time linear state space models and equidistantly observed multivariate Lévy-driven continuous-time autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard… (More)

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