Maximal inequalities via bracketing with adaptive truncation
Maximal Weak-Type Inequality for Orthogonal Harmonic Functions and Martingales
Assume that u, v are conjugate harmonic functions on the unit disc of ℂ, normalized so that u(0) = v(0) = 0. Let u*, |v|* stand for the one- and two-sided Brownian maxima of u and v, respectively. The paper contains the proof of the sharp weak-type estimate ℙ(|v|* ≥ 1)≤ (1 + 1/3² + 1/5² + 1/7² + ...)/(1 - 1/3² + 1/5² - 1/7² + ...) 𝔼u*. Actually, this estimate is shown to be true in the more general setting of differentially subordinate harmonic functions defined...
Maximum length of a series in a Markovian binary sequence with an application to the description of a basketball game
The recurrence formulas for the probability distribution function of the maximum length of a series of 1's in a binary 0-1 Markovian sequence are analysed and the limiting distribution estimated. The result is used to test a semi-Markov model of basketball games.
Maximum principle and comparison theorem for quasi-linear stochastic PDE's.
Maximum process problems in optimal control theory.
Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices.
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.
Mean quadratic convergence of signed random measures
We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper.
Mean stability of a stochastic difference equation
A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, the techniques for obtaining its properties are not, and we make use of the theory of abstract Banach algebras and weighted spaces. It is hoped...
Measurability of stochastic process and approximate continuity of its correlation function.
Measure attractors for stochastic Navier-Stokes equations.
Measures defined by Markov times
Median for metric spaces
We consider a Köthe space of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications....
Meilleures approximations et médianes conditionnelles
Mesurabilité des débuts et théorème de section : le lot à la portée de toutes les bourses
Mesure de Hausdorff de la trajectoire de certains processus à accroissements indépendants et stationnaires
Mesures à accroissements indépendants et P.A.I. non homogènes
Mesures aléatoires localement finies