Martingales relatives
Martingales sur le cercle
Mathematical modelling of tumour angiogenesis and the action of angiostatin as a protease inhibitor.
Maxima and minima of stationary random sequences under a local dependence restriction.
Maxima of the cells of an equiprobable multinomial.
Maximal brownian motions
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....
Maximal displacement for bridges of random walks in a random environment
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...
Maximal inequalities for Bessel processes.
Maximal Inequalities for Stochastic Integrals
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...