Clark representation formula for the solution to equation with interaction
Teoriâ slučajnyh processov, Tome 25 (2020) no. 2, pp. 9-14.

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

In this paper an analogue of the Clark-Ocone representation for solution to measure-valued equation with interaction is studied. It is proved that the integrand is absolutely continuous with respect to Lebesgue measure.
Keywords: Stochastic differential equations with interaction, Clark representation, Clark-Ocone formula.
@article{THSP_2020_25_2_a1,
     author = {Jasmina {\DJ}or{\dj}evi\'c and Andrey Dorogovtsev},
     title = {Clark representation formula for the solution to equation with interaction},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {9--14},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a1/}
}
TY  - JOUR
AU  - Jasmina Đorđević
AU  - Andrey Dorogovtsev
TI  - Clark representation formula for the solution to equation with interaction
JO  - Teoriâ slučajnyh processov
PY  - 2020
SP  - 9
EP  - 14
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a1/
LA  - en
ID  - THSP_2020_25_2_a1
ER  - 
%0 Journal Article
%A Jasmina Đorđević
%A Andrey Dorogovtsev
%T Clark representation formula for the solution to equation with interaction
%J Teoriâ slučajnyh processov
%D 2020
%P 9-14
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a1/
%G en
%F THSP_2020_25_2_a1
Jasmina Đorđević; Andrey Dorogovtsev. Clark representation formula for the solution to equation with interaction. Teoriâ slučajnyh processov, Tome 25 (2020) no. 2, pp. 9-14. http://geodesic.mathdoc.fr/item/THSP_2020_25_2_a1/

[1] J. M. C. Clark, “The representation of functionals of Brownian motion by stochastic integrals”, Ann. Math. Statist., 41:4 (1970), 1282–1295

[2] A. A. Dorogovtsev, Meroznachnye protsessy i stokhasticheskie potoki [Measure-valued processes and stochastic flows], Proceedings of Institute of Mathematics of NAS of Ukraine. Mathematics and its Applications, 66, Institut Matematiki, Kiev, 2007 (Russian)

[3] J. Ðorđević, S. Jankovic, “On a class of backward stochastic Volterra integral equations”, Applied Mathematics Letters, 26 (2013), 1192–1197

[4] T. Komatsu, “On the partial hypoellipticity of SDEs on Hilbert spaces”, Theory of Stochastic Processes, 10 (26):3-4 (2004), 67–73

[5] D. Nualart, The Malliavin Calculus and Related Topics, eds. 2nd ed., Springer, 2006

[6] G. Pisier, Martingales in Banach Spaces, Cambridge Univ. Press, 2016

[7] S. Janković, M. Jovanović, J. Ðorđević, “Perturbed backward stochastic differential equations”, Mathematical and Computer Modeling, 55 (2012), 1734–1745