Titlebook: Séminaire de Probabilités XXXVIII; Michel Émery,Michel Ledoux,Marc Yor Book 2005 Springer-Verlag Berlin Heidelberg 2005 Brownian motion.Ga

美食家

https://doi.org/10.1007/b104072Brownian motion; Gaussian process; Lévy process; Markov process; Martingale; Ornstein-Uhlenbeck process; P

idiopathic

,Tanaka’s Construction for Random Walks and Lévy Processes,Tanaka’s construction gives a pathwise construction of “random walk conditioned to stay positive”, and has recently been used in [3] and [8] to establish other results about this process. In this note we give a simpler proof of Tanaka’s construction using a method which also extends to the case of Lévy processes.

小口啜饮

,A Martingale Review of some Fluctuation Theory for Spectrally Negative Lévy Processes,We give a review of some fluctuation theory for spectrally negative Lévy processes using for the most part martingale theory. The methodology is based on the techniques found in Kyprianou and Palmowski (2003) which deal with similar issues for a general class of Markov additive processes.

Anthology

FLIP

,Some Martingales Associated to Reflected Lévy Processes,We introduce and describe several classes of martingales based on reflected Lévy processes. We show how these martingales apply to various problems, in particular in fluctuation theory, as an alternative to the use of excursion methods. Emphasis is given to the case of spectrally negative processes.

全等

,Propriété de Choquet-Deny et fonctions harmoniques sur les hypergroupes commutatifs,Dans cet article, on prouve un résultat de type Choquet-Deny sur les hypergroupes commutatifs: les seules fonctions harmoniques continues bornées des marches aléatoires irréductibles sont les fonctions constantes. On en déduit la description de la frontière de Martin par une méthode de relativisation.

Progesterone

Positive Bilinear Mappings Associated with Stochastic Processes,On some vector spaces of adapted stochastic processes, we define increasing families of positive bilinear forms, which generalize the usual square brackets [.,.] and angle brackets .. We study the corresponding Hardy spaces especially for . = 1 or 2, and extend to this abstract framework results of Fefferman type from martingale theory.

伸展

An Almost Sure Approximation for the Predictable Process in the Doob-Meyer Decomposition Theorem,We construct the Doob-Meyer decomposition of a submartingale as a pointwise superior limit of decompositions of discrete submartingales suitably built upon discretizations of the original process. This gives, in particular, a direct proof of predictability of the increasing process in the Doob-Meyer decomposition.

Consensus

Rotations and Tangent Processes on Wiener Space,The paper considers (a) Representations of measure preserving transformations (“rotations”) on Wiener space, and (b) The stochastic calculus of variations induced by parameterized rotations.: “Directional derivatives” ., “vector fields” or “tangent processes” . and flows of rotations.

发展