Level crossings of a random polynomial with hyperbolic elements.
Long-memory stable Ornstein-Uhlenbeck processes.
Markov chains approximation of jump–diffusion stochastic master equations
Quantum trajectories are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called Belavkin equations or Stochastic Master equations, are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems...
Mean number of real zeros of a random hyperbolic polynomial.
Mean number of real zeros of a random trigonometric polynomial. IV.
Mean number of real zeros of a random trigonometric polynomial. III.
Mesures aléatoires stationnaires et mesure de Palm
Mesures aléatoires stationnaires sur un espace produit
Mesures de Radon sur et mesures cylindriques
Metric unconditionality and Fourier analysis
We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between and . These...
Multiscale estimation of cell kinetics.
Multi-variate correlation and mixtures of product measures
Total correlation (‘TC’) and dual total correlation (‘DTC’) are two classical ways to quantify the correlation among an -tuple of random variables. They both reduce to mutual information when . The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part considers the structural implications when a joint distribution has small TC or DTC. If , then is...
Notes on dependence with complete connections
Number of real roots of a random trigonometric polynomial.
On a class of linear models.
This paper is concerned with classification criteria, asymptotic behaviour and stationarity of a non-Markovian model with linear transition rule, called a linear OM-chain. This problems are solved by making use of the structure of the stochastic matrix appearing in the definition of such a model. The model studied includes as special cases the Markovian model as well as the linear learning model, and has applications in psychological and biological research, in control theory, and in adaptation...
On a Generalization of the Cauchy Equation.
On different classes of algebraic polynomials with random coefficients.
On logarithmic information in point processes
On mean numbers of passage times in small balls of discretized Itô processes.
On Paszkiewicz-type criterion for a.e. continuity of processes in -spaces
In this paper we consider processes Xₜ with values in , p ≥ 1 on subsets T of a unit cube in ℝⁿ satisfying a natural condition of boundedness of increments, i.e. a process has bounded increments if for some non-decreasing f: ℝ₊ → ℝ₊ ||Xₜ-Xₛ||ₚ ≤ f(||t-s||), s,t ∈ T. We give a sufficient criterion for a.s. continuity of all processes with bounded increments on subsets of a given set T. This criterion turns out to be necessary for a wide class of functions f. We use a geometrical Paszkiewicz-type...