A class of remarkable submartingales

Ashkan Nikeghbali

Stochastic Processes and their Applications, 2006, vol. 116, issue 6, 917-938

Abstract: In this paper, we consider the special class of positive local submartingales (Xt) of the form Xt=Nt+At, where the measure is carried by the set {t:Xt=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 for studying them. In particular, we establish some martingale characterizations for these processes and compute explicitly some distributions involving the pair (Xt,At). We also associate with X a solution to the Skorokhod's stopping problem for probability measures on the positive half-line.

Keywords: Submartingales; Azema's; submartingale; Bessel; processes; Inequalities; General; theory; of; stochastic; processes; Skorokhod's; stopping; problem (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (12)

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