Geodesic
Two-Parameter Stochastic Volterra Equations
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 525-537

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

We study two-parameter stochastic Volterra equations containing integrals over strong martingales and fields of bounded variation. For such equations, we prove the existence and uniqueness theorems for solutions with trajectories in the space of Borel functions which are locally square-integrable with respect to a locally finite measure. Under additional conditions on the coefficients of the equation, we prove the existence of a modification of the solution with trajectories continuous on the right and without discontinuities of the second kind.
Mots-clés : stochastic Volterra equation, martingale
Keywords: Borel function, metric separable space, stochastic integral, Hölder's inequality. 
@article{MZM_2009_86_4_a4,
     author = {N. A. Kolodij},
     title = {Two-Parameter {Stochastic} {Volterra} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {525--537},
     publisher = {mathdoc},
     volume = {86},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a4/}
}
TY  - JOUR
AU  - N. A. Kolodij
TI  - Two-Parameter Stochastic Volterra Equations
JO  - Matematičeskie zametki
PY  - 2009
SP  - 525
EP  - 537
VL  - 86
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a4/
LA  - ru
ID  - MZM_2009_86_4_a4
ER  - 
%0 Journal Article
%A N. A. Kolodij
%T Two-Parameter Stochastic Volterra Equations
%J Matematičeskie zametki
%D 2009
%P 525-537
%V 86
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a4/
%G ru
%F MZM_2009_86_4_a4
N. A. Kolodij. Two-Parameter Stochastic Volterra Equations. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 525-537. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a4/