A class of remarkable submartingales

2005/05/31 by Ashkan Nikeghbali · 1 citation
Mathematics · #math.PR #msc:05C38 #msc:15A15 #msc:15A18

paper · pdf

published as Stochastic Processes and their applications; 116 - p.917-938 (2006) · Typos corrected. Close to the published version

arxiv created 2007/08/03 · arxiv updated 2009/12/01

Abstract

In this paper, we consider the special class of positive local submartingales (X_t) of the form: X_t=N_t+A_t, where the measure (dA_t) is carried by the set t: X_t=0. We show that many examples of stochastic processes studied in the literature are in this class and propose a unified approach based on martingale techniques to study them. In particular, we establish some martingale characterizations for these processes and compute explicitly some distributions involving the pair (X_t,A_t). We also associate with X a solution to the Skorokhod's stopping problem for probability measures on the positive half-line.

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