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 : https://doi.org/10.5802/ambp.238
Classification : 26A33,  60H15
Mots clés : EDPS, Dérivation fractionnaire, mesure de Poisson
@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},
     mrnumber = {2418012},
     zbl = {1154.26008},
     language = {en},
     url = {www.numdam.org/item/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://www.numdam.org/item/AMBP_2008__15_1_43_0/

[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 | Article | MR 1624076 | Zbl 0934.60055

[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 | Article | Zbl 0939.60064

[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 1013.60044

[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 2354419 | Zbl pre05205607

[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 | Article | MR 2172885 | Zbl 1078.60048

[6] Fournier, N. Malliavin calculus for parabolic SPDEs with jumps, Stochastic Processes and Their Applications, Volume 87 (2000), pp. 115-147 | Article | MR 1751168 | Zbl 1045.60067

[7] Ikeda, N.; Watanabe, S. Stochastic differential equations and diffusion processes, North-Holland Publishing Company. Mathematical Library 24., Holland, 1989 | MR 1011252 | Zbl 0684.60040

[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 1658022 | Zbl 0924.34008

[9] Walsh., J.B. An Introduction to stochastic partial differential equations, Lecture Notes in Mathematics 1180, Springer Berlin / Heidelberg, 1986, pp. 266-437 | MR 876085 | Zbl 0608.60060

[10] Zabczyk., J. Symmetric solutions of semilinear stochastic equations, Lecture Notes in Mathematics 1390, Springer Berlin / Heidelberg, 1988, pp. 237-256 | MR 1019609 | Zbl 0701.60060