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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)
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)
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)