Stochastic fractional partial differential equations driven by Poisson white noise
[Équations aux dérivées partielles fractionnaires stochastiques dirigées par un bruit poissonnien]
Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 1, pp. 43-55.

On étudie une équation aux dérivées partielles stochastiques fractionnaires d’ordre α>1 dirigée par une mesure de Poisson compensée. On montre l’existence et l’unicité de la solution et on étudie la régularité de ses trajectoires.

We study a stochastic fractional partial differential equations of order α>1 driven by a compensated Poisson measure. We prove existence and uniqueness of the solution and we study the regularity of its trajectories.

DOI : 10.5802/ambp.238
Classification : 26A33, 60H15
Keywords: Stochastic partial differential equations, fractional derivative operator, Poisson measure.
Mot clés : EDPS, Dérivation fractionnaire, mesure de Poisson
Hajji, Salah 1

1 Department of Mathematics Faculty of Sciences Semlalia Cadi Ayyad University BP. 2390 Marrakesh, MOROCCO.
@article{AMBP_2008__15_1_43_0,
     author = {Hajji, Salah},
     title = {Stochastic fractional partial differential equations driven by {Poisson} white noise},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {43--55},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {15},
     number = {1},
     year = {2008},
     doi = {10.5802/ambp.238},
     zbl = {1154.26008},
     mrnumber = {2418012},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/ambp.238/}
}
TY  - JOUR
AU  - Hajji, Salah
TI  - Stochastic fractional partial differential equations driven by Poisson white noise
JO  - Annales mathématiques Blaise Pascal
PY  - 2008
SP  - 43
EP  - 55
VL  - 15
IS  - 1
PB  - Annales mathématiques Blaise Pascal
UR  - http://archive.numdam.org/articles/10.5802/ambp.238/
DO  - 10.5802/ambp.238
LA  - en
ID  - AMBP_2008__15_1_43_0
ER  - 
%0 Journal Article
%A Hajji, Salah
%T Stochastic fractional partial differential equations driven by Poisson white noise
%J Annales mathématiques Blaise Pascal
%D 2008
%P 43-55
%V 15
%N 1
%I Annales mathématiques Blaise Pascal
%U http://archive.numdam.org/articles/10.5802/ambp.238/
%R 10.5802/ambp.238
%G en
%F AMBP_2008__15_1_43_0
Hajji, Salah. Stochastic fractional partial differential equations driven by Poisson white noise. Annales mathématiques Blaise Pascal, Tome 15 (2008) no. 1, pp. 43-55. doi : 10.5802/ambp.238. http://archive.numdam.org/articles/10.5802/ambp.238/

[1] Albeverio, S.; Wu, J.-L.; Zhang, T.-S. Parabolic SPDEs driven by Poisson White Noise, Stochastic Processes and Their Applications, Volume 74 (1998), pp. 21-36 | DOI | MR | Zbl

[2] Bié, E. Saint Loubert Etude d’une EDPS conduite par un bruit Poissonnien, Probability Theory and related fields, Volume 111 (1998), pp. 287-321 | DOI | Zbl

[3] Dalang, R.; Mueller, C. Some non-linear s.p.d.e.’s that are second order in time, Electron. J. Probab., Volume 8 (2003), pp. 1-21 | Zbl

[4] Debbi, L. On some properties of a High Order fractional differential operator which is not in general selfadjoint, Applied Mathematical Sciences, Volume 1,27 (2007), pp. 1325-1339 | MR

[5] Debbi, L.; Dozzi, M. On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension, Stoc. Proc. Appl., Volume 115 (2005), pp. 1764-1781 | DOI | MR | Zbl

[6] Fournier, N. Malliavin calculus for parabolic SPDEs with jumps, Stochastic Processes and Their Applications, Volume 87 (2000), pp. 115-147 | DOI | MR | Zbl

[7] Ikeda, N.; Watanabe, S. Stochastic differential equations and diffusion processes, North-Holland Publishing Company. Mathematical Library 24., Holland, 1989 | MR | Zbl

[8] Podlubny, I. Fractional Differential equations: an Introduction to Fractional Derivatives, Fractional Differential equations, to Methods of Their Solution and Some of their Applications, Academic Press, San Diego, CA., 1999 | MR | Zbl

[9] Walsh., J.B. An Introduction to stochastic partial differential equations, Lecture Notes in Mathematics 1180, Springer Berlin / Heidelberg, 1986, pp. 266-437 | MR | Zbl

[10] Zabczyk., J. Symmetric solutions of semilinear stochastic equations, Lecture Notes in Mathematics 1390, Springer Berlin / Heidelberg, 1988, pp. 237-256 | MR | Zbl

Cité par Sources :