Convergence of lattice trees to super-Brownian motion above the critical dimension.
Convergence of martingales on manifolds of negative curvature
Convergence of randomly oscillating point patterns to the Poisson point process
Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical...
Convergence of simple random walks on random discrete trees to brownian motion on the continuum random tree
In this article it is shown that the brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete n-vertex ordered graph trees whose search-depth functions converge to the brownian excursion as n→∞. We prove both a quenched version (for typical realisations of the trees) and an annealed version (averaged over all realisations of the trees) of our main result. The assumptions of the article cover the important example of simple random walks...
Convergence of stochastic processes [Abstract of thesis]
Convergence of Submartingales to an Increasing Process under Discretization of Filtrations
Convergence of the -series for stationary sequences.
Convergence of Tight Asymptotic Martingales in a Banach Space.
Convergence of unbounded multivalued supermartingales in the Mosco and slice topologies.
Convergence of values in optimal stopping and convergence of optimal stopping times.
Convergence of weighted sums of independent random variables and an extension to Banach space-valued random variables.
Convergence presque sûre de martingales multivoques
Convergence rates for quadratic forms of random variables
Convergence rates for the full gaussian rough paths
Under the key assumption of finite -variation, , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), resp. , we recover and extend the respective results of (Trans. Amer. Math. Soc.361 (2009) 2689–2718) and (Ann. Inst. Henri Poincasé Probab. Stat.48(2012) 518–550). In particular, we establish an a.s. rate , any , for Wong–Zakai and Milstein-type...
Convergence rates for weighted sums of random variables with random indices
Convergence to zero and boundedness of operator-normed sums of random vectors with application to autoregression processes.
Convergences de Martingales a valeurs Vectorielles
Convex analysis for sets of local martingales measures
Convex concentration inequalities and forward-backward stochastic calculus.
Convex hulls, Sticky particle dynamics and Pressure-less gas system
We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities with negative jumps. We show the existence of a stochastic process and a forward flow satisfying and , where is the law of and is the velocity of particle at time . Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map is the entropy solution of a scalar conservation law where the flux represents the particles...