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With the help of two Skorokhod embeddings, we construct martin-gales which enjoy the Brownian scaling property and the (inhomogeneous) Markov property. The second method necessitates randomization, but allows to reach any law with finite moment of order 1, centered, as the distribution of such a martingale at unit time. The first method does not necessitate(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract We present some limit theorems for the normalized laws (with respect to functionals involving last passage times at a given level a up to time t) of a large class of null recurrent diffusions. Our results rely on hypotheses on the Lévy measure of the diffusion inverse local time at 0. As a special(More)
The model consists of a signal process X which is a general Brownian diffusion process and an observation process Y , also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process Y is observed from time 0 to s > 0 at discrete times and aim to estimate, conditionally on these observations, the probability(More)
We compute the persistence exponent of the integral of a stable Lévy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Z. Shi (2003). Along the way, we investigate the law of the stable process L evaluated at the first time its integral X hits zero, when the bivariate process (X, L) starts from a coordinate(More)
This article analyzes the status of two classical one-particle probability density function (PDF) descriptions of the dynamics of discrete particles dispersed in turbulent flows. The first PDF formulation considers only the process made up by particle position and velocity Z(p)=(x(p),U(p)) and is represented by its PDF p(t; y(p),V(p)) which is the solution(More)
Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real Lévy process. This gives a simple and unified proof of several results in the literature, old and recent. We also provide a full description of the corresponding Green functions. As a by-product, we compute the(More)
We propose a mathematical model for one pattern of charts studied in technical analysis: in a phase of consolidation, the price of a risky asset goes down ξ times after hitting a resistance level. We construct a mathematical strategy and we calculate the expectation of the wealth for the logaritmic utility function. Via simulations, we compare the strategy(More)