Geodesic
On the theory of backward stochastic differential equations and their applications
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2015), pp. 15-46

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we discuss conditions of existence of solutions of backward stochastic differential equations with respect to general filtrations. A solution of a linear backward stochastic differential equation is found using classical theory of differential equations. We also study a special class of backward stochastic differential equations. Using solution properties of this type of equations, we give a new direct proof of Doob-Meyer theorem on a decomposition of a supermartingale from class $DL$ into a difference of a martingale and an increasing predictive process. We also prove a new theorem on transposition of an integral of a stochastic process and a conditional mathematical expectation.
Keywords: backward stochastic differential equation, Doob-Meyer decomposition, supermartingale.
Mots-clés : martingales 
@article{VTPMK_2015_1_a1,
     author = {S. Yu. Kashayeva},
     title = {On the theory of backward stochastic differential equations and their applications},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {15--46},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2015_1_a1/}
}
TY  - JOUR
AU  - S. Yu. Kashayeva
TI  - On the theory of backward stochastic differential equations and their applications
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2015
SP  - 15
EP  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2015_1_a1/
LA  - ru
ID  - VTPMK_2015_1_a1
ER  - 
%0 Journal Article
%A S. Yu. Kashayeva
%T On the theory of backward stochastic differential equations and their applications
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2015
%P 15-46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTPMK_2015_1_a1/
%G ru
%F VTPMK_2015_1_a1
S. Yu. Kashayeva. On the theory of backward stochastic differential equations and their applications. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2015), pp. 15-46. http://geodesic.mathdoc.fr/item/VTPMK_2015_1_a1/