Independence of time and position for a random walk.
Inégalités en norme pour le produit des suprema de plusieurs martingales arrêtées à des temps aléatoires. Inégalités avec poids
Inferring the residual waiting time for binary stationary time series
For a binary stationary time series define to be the number of consecutive ones up to the first zero encountered after time , and consider the problem of estimating the conditional distribution and conditional expectation of after one has observed the first outputs. We present a sequence of stopping times and universal estimators for these quantities which are pointwise consistent for all ergodic binary stationary processes. In case the process is a renewal process with zero the renewal state...
Integration of the optimal risk in a stopping problem with absorption
Intertwining of birth-and-death processes
It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of the eigenvalues,...
Introduction au calcul stochastique