Martingales sur le cercle
A characterization of the transport property is given. New properties for strongly nonatomic probabilities are established. We study the relationship between the nondifferentiability of a real function f and the fact that the probability measure , where f*(x):=(x,f(x)) and λ is the Lebesgue measure, has the transport property.
We are interested in the rate function of the moderate deviation principle for the two-sample matching problem. This is related to the determination of 1-Lipschitz functions with maximal variance. We give an exact solution for random variables which have normal law, or are uniformly distributed on the Euclidean ball.
A mathematical model of mixing food in rumen is presented. The model is based on the idea of the Baker Transformation, but exhibits some different phenomena: the transformation does not mix points at all in some parts of the phase space (and under some conditions mixes them strongly in other parts), as observed in ruminant animals.
We derive the limiting matrix kernels for the Gaussian orthogonal and symplectic ensembles scaled at the edge, with proofs of convergence in the operator norms that ensure convergence of the determinants.
Let Z=(X, Y) be a planar brownian motion, the filtration it generates, andBa linear brownian motion in the filtration . One says thatB(or its filtration) is maximal if no other linear -brownian motion has a filtration strictly bigger than that ofB. For instance, it is shown in [In Séminaire de Probabilités XLI 265–278 (2008) Springer] that B is maximal if there exists a linear brownian motion C independent of B and such that the planar brownian motion (B, C) generates the same filtration asZ....
It is well known that the distribution of simple random walks on ℤ conditioned on returning to the origin after 2n steps does not depend on p=P(S1=1), the probability of moving to the right. Moreover, conditioned on {S2n=0} the maximal displacement maxk≤2n|Sk| converges in distribution when scaled by √n (diffusive scaling). We consider the analogous problem for transient random walks in random environments on ℤ. We show that under the quenched law Pω (conditioned on the environment ω), the maximal...
Some maximal inequalities for quadratic forms of independent and linearly negative quadrant dependent fuzzy random variables are established. Strong convergence of such quadratic forms are proved based on the martingale theory. A weak law of large numbers for linearly negative quadrant dependent fuzzy random variables is stated and proved.