Long-range dependence in a Cox process directed by a Markov renewal process.
Long-range dependence through gamma-mixed Ornstein-Uhlenbeck process.
Long-range self-avoiding walk converges to α-stable processes
We consider a long-range version of self-avoiding walk in dimension d > 2(α ∧ 2), where d denotes dimension and α the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to brownian motion for α ≥ 2, and to α-stable Lévy motion for α < 2. This complements results by Slade [J. Phys. A21 (1988) L417–L420], who proves convergence to brownian motion for nearest-neighbor self-avoiding walk in high dimension.
Long-term behavior for superprocesses over a stochastic flow.
Look-ahead Levinson- and Schur-type recurrences in the Padé table.
Loop-erased random walks, spanning trees and Hamiltonian cycles.
Loop-erased walks intersect infinitely often in four dimensions.
Loop-free Markov chains as determinantal point processes
We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.
Lower bounds on //K...//1...... For some contractions K of L² (...), with applications to Markov operators.
Lower estimates for random walks on a class of amenable -adic groups.
Lyapunov exponents for the parabolic Anderson model.
-estimation in nonlinear regression for longitudinal data
The longitudinal regression model where is the th measurement of the th subject at random time , is the regression function, is a predictable covariate process observed at time and is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth -estimator of unknown parameter .
Majoration dans du type Métivier-Pellaumail pour les semimartingales
Majorization of sequences, sharp vector Khinchin inequalities, and bisubharmonic functions
Let , , where the are independent random vectors, each uniformly distributed on the unit sphere in ℝⁿ, and are real constants. We prove that if is majorized by in the sense of Hardy-Littlewood-Pólya, and if Φ: ℝⁿ → ℝ is continuous and bisubharmonic, then EΦ(X) ≤ EΦ(Y). Consequences include most of the known sharp Khinchin inequalities for sums of the form X. For radial Φ, bisubharmonicity is necessary as well as sufficient for the majorization inequality to always hold. Counterparts...
Majorizing Measures and Ultrametric Spaces
Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.
Malliavin calculus for two-parameter processes
Malliavin calculus in Lev́y spaces and applications to finance.
Manifold indexed fractional fields
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
Manifold indexed fractional fields∗
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps