A new proof of Kellerer’s theorem

Hirsch, Francis, and Roynette, Bernard. "A new proof of Kellerer’s theorem." ESAIM: Probability and Statistics 16 (2012): 48-60. <http://eudml.org/doc/222467>.

@article{Hirsch2012,
abstract = {In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.},
author = {Hirsch, Francis, Roynette, Bernard},
journal = {ESAIM: Probability and Statistics},
keywords = {Convex order; 1-martingale; peacock; Fokker-Planck equation; Kellerer's theorem; convex order; associated processes, 1-martingale},
language = {eng},
month = {3},
pages = {48-60},
publisher = {EDP Sciences},
title = {A new proof of Kellerer’s theorem},
url = {http://eudml.org/doc/222467},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Hirsch, Francis
AU - Roynette, Bernard
TI - A new proof of Kellerer’s theorem
JO - ESAIM: Probability and Statistics
DA - 2012/3//
PB - EDP Sciences
VL - 16
SP - 48
EP - 60
AB - In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
LA - eng
KW - Convex order; 1-martingale; peacock; Fokker-Planck equation; Kellerer's theorem; convex order; associated processes, 1-martingale
UR - http://eudml.org/doc/222467
ER -