Processus multistables (propriétés locales et estimation)

Nous étudions les propriétés probabilistes, trajectorielles et statistiques des processus stochastiques multistables, qui sont tangents en chaque point a un processus stable. Ils possèdent ainsi une intensité de sauts et une régularité locale qui varient au cours du temps. Nous nous intéressons dans un premier temps aux processus pouvant être définis par une moyenne mobile et possédant la propriété d'être localisables, c'est-a-dire d'être tangents en loi a un processus en chaque point. Des critères assurant la localisabilite, ainsi qu'une méthode de simulation de tels processus sont donnes. Nous proposons ensuite une nouvelle construction et des critères de localisabilite des processus multistables a l'aide d'une representation de type Ferguson-Klass-LePage. Pour les processus obtenus, nous étudions certaines propriétés probabilistes et trajectorielles. En particulier, nous caractérisons le comportement asymptotique des accroissements des processus multistables, ainsi que leur regularite Holderienne. Enfin, nous proposons des estimateurs de la fonction de stabilité et de la fonction de localisabilite. La consistance au sens de la convergence Lp est prouvée. Les performances des estimateurs sont illustrées sur des séries simulées suivant deux modèles : le mouvement de Levy multistable et le mouvement linéaire multifractionnaire multistable.This PhD thesis deals with some probabilistic, pathwise and statistical properties of multistable stochastic processes, which are tangent at any point to a stable process. Their intensity of jumps and their local regularity are varying with time. We rst consider the processes possibly dened as a moving average which are localisable, that is they are tangent to a non-trivial process at any point. We give general conditions which ensure that the moving average is localisable and we characterize the nature of the associated tangent process. We also consider the problem of path synthesis, for which we give both theoretical results and numerical simulations. We present then a dierent construction of the multistable processes, based on the Ferguson-Klass-LePage series representation. We consider various particular cases of interest, including multistable Levy motion and linear multistable multifractional motion. We study then some probabilistic properties. In particular, we describe the behavior of the incremental moments and the pointwise Holder exponent. We compute the precise value of the almost sure Holder exponent in the case of the multistable Levy motion. Finally, we give two estimators of the stability and the localisability functions, and we prove the consistency of those two estimators. We illustrate these convergences with the Levy multistable process and the Linear Multifractional Multistable MotionNANTES-BU Sciences (441092104) / SudocSudocFranceF

Convergent Enantioselective Synthesis of Vinigrol, an Architecturally Novel Diterpenoid with Potent Platelet Aggregation Inhibitory and Antihypertensive Properties. 1. Application of Anionic Sigmatropy to Construction of the Octalin Substructure

The coupling of building blocks 15 and 36e in the presence of MgBr2·OEt2 at 0 °C proceeds with an exo stereoselectivity (3.2:1) considerably more advantageous for the acquisition of carbinol 37e than in the absence of the additive (exo/endo = 1:5.7). The pivotal transformation that sets all of the relevant stereocenters of the cis-octalin 55 is the oxyanionic-accelerated [3,3]-sigmatropic rearrangement of 37e. A salient feature is the structurally enforced adoption of a boatlike transition state that serves to properly set four vicinal methine hydrogens in an all-cis arrangement. The ensuing conversion of 55 into iodo sulfone 62 has permitted X-ray crystallographic confirmation of all absolute stereochemical assignments since the isopropyl substituent was initially installed enantioselectively via the Evans oxazolidinone protocol. No intramolecular anionic cyclization of 62 to generate the tricyclic framework was seen. This absence of reactivity is attributed to conformational factors that inhibit attainment of the proper SN2 reaction trajectory

Millimeter-wave pulsed heating in vitro: cell mortality and heat shock response

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