More on existence and uniqueness of decomposition of excessive functions and measures into extremes
Most random walks on nilpotent groups are mixing
Let G be a second countable locally compact nilpotent group. It is shown that for every norm completely mixing (n.c.m.) random walk μ, αμ + (1-α)ν is n.c.m. for 0 < α ≤ 1, ν ∈ P(G). In particular, a generic stochastic convolution operator on G is n.c.m.
Mouvement brownien et inégalité de Hardy dans
Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation.
Multifractal analysis of infinite products of stationary jump processes.
Multifractal properties of the sets of zeroes of Brownian paths
We study Brownian zeroes in the neighborhood of which one can observe a non-typical growth rate of Brownian excursions. We interpret the multifractal curve for the Brownian zeroes calculated in [6] as the Hausdorff dimension of certain sets. This provides an example of the multifractal analysis of a statistically self-similar random fractal when both the spacing and the size of the corresponding nested sets are random.
Multiparameter pointwise ergodic theorems for Markov operators on L∞.
Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p < ∞ the averagesAnf = (n + 1)-d Σ0≤ni≤n P1n1 P2n2 ... Pdnd f (n ≥ 0)converge almost everywhere if and only if there exists an invariant and equivalent finite measure λ for which the Radon-Nikodym derivative v = dλ/dμ is in the dual space Lp'(X,F,μ). Next we study the case in...
Multiple points of Markov processes in a complete metric space
Multiple recurrence for discrete time Markov processes
Multiple recurrence for discrete time Markov processes. II
Multiple scale analysis of spatial branching processes under the Palm distribution.
Multiple space-time scale analysis for interacting branching models.
Multiplicative excessive measures and duality between equations of Boltzmann and of branching processes
Multiplicative functionals and the stable topology
Multiplicative functionals of dual processes
Let and be a pair of dual standard Markov processes. We associate to each exact multiplicative function , of a unique exact , of in a natural manner. Any , is assumed to satisfy . The map is bijective and multiplicative in the sense that: .This correspondence is studied in some detail and several important examples are discussed.These results are then applied to study additive functionals.
Multiplicities of a random sausage
Multiscale Piecewise Deterministic Markov Process in infinite dimension: central limit theorem and Langevin approximation
In [A. Genadot and M. Thieullen, Averaging for a fully coupled piecewise-deterministic markov process in infinite dimensions. Adv. Appl. Probab. 44 (2012) 749–773], the authors addressed the question of averaging for a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimensions. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuations of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated...
Multi-scaled diffusion-approximation. Applications to wave propagation in random media
Multi-scaled diffusion-approximation. Applications to wave propagation in random media.
In this paper a multi-scaled diffusion-approximation theorem is proved so as to unify various applications in wave propagation in random media: transmission of optical modes through random planar waveguides; time delay in scattering for the linear wave equation; decay of the transmission coefficient for large lengths with fixed output and phase difference in weakly nonlinear random media.
Multivariate Markov Families of Copulas
For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples...