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Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)

- A. Greven, P. Pfaffelhuber, A. Winter
- Mathematics
- 1 September 2009

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure… Expand

Large Deviations for a Random Walk in Random Environment

- A. Greven, F. Hollander
- Mathematics
- 1 July 1994

Let $\omega = (p_x)_{x\in\mathbb{Z}}$ be an i.i.d. collection of (0, 1)-valued random variables. Given $\omega$, let $(X_n)_{n \geq 0}$ be the Markov chain on $\mathbb{Z}$ defined by $X_0 = 0$ and… Expand

Marked metric measure spaces

- A. Depperschmidt, A. Greven, P. Pfaffelhuber
- Mathematics
- 21 January 2011

A marked metric measure space (mmm-space) is a triple $(X,r,μ)$, where $(X,r)$ is a complete and separable metric space and $μ$ is a probability measure on $X \times I$ for some Polish space $I$ of… Expand

Comparison of interacting diffusions and an application to their ergodic theory

- J. T. Cox, K. Fleischmann, A. Greven
- Mathematics
- 1 August 1996

SummaryA general comparison argument for expectations of certain multitime functionals of infinite systems of linearly interacting diffusions differing in the diffusion coefficient is derived. As an… Expand

Phase transitions for the long-time behaviour of interacting diffusions

- A. Greven, F. Hollander
- Mathematics
- 6 November 2006

Let ({Xi(t)}i∈Zd)t≥0 be the system of interacting diffusions on [0,∞) defined by the following collection of coupled stochastic differential equations: dXi(t) = ∑ j∈Zd a(i, j)[Xj(t)−Xi(t)] dt+ √… Expand

Ergodic theorems for infinite systems of locally interacting diffusions

Here g: [0, 1] --+ RI satisfies g > 0 on (0, 1), g(0) = g(l) = 0, g is Lipschitz, a(i,j) is an irreducible random walk kernel on Zd and {wi(t), i E Zd} is a family of standard, independent Brownian… Expand

Collision local time of transient random walks and intermediate phases in interacting stochastic systems

- M. Birkner, A. Greven, Hollander den WThF
- Mathematics
- 1 November 2011

In a companion paper (M. Birkner, A. Greven, F. den Hollander, Quenched LDP for words in a letter sequence, Probab. Theory Relat. Fields 148 , no. 3/4 (2010), 403-456), a quenched large deviation… Expand

Tree-valued Fleming–Viot dynamics with mutation and selection

- A. Depperschmidt, A. Greven, P. Pfaffelhuber
- Mathematics
- 4 January 2011

The Fleming-Viot measure-valued diffusion is a Markov process describing the evolution of (allelic) types under mutation, selection and random reproduction. We enrich this process by genealogical… Expand

Mutually catalytic super branching random walks: large finite systems and renormalization analysis

Introduction Results: Longtime behavior of large finite systems Results: Renormalization analysis and corresponding basic limiting dynamics Results: Application of renormalization to large scale… Expand

Spatial Fleming-Viot Models with Selection and Mutation

Introduction.- Emergence and fixation in the F-W model with two types.- Formulation of the multitype and multiscale model.- Formulation of the main results in the general case.- A Basic Tool: Dual… Expand

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