Existence for stochastic sweeping process with fractional Brownian motion

Authors

  • Tayeb BLOUHI Faculty of Mathematics and Computer Science, Department of Mathematics, University of Science and Technology, Mohamed-Boudiaf El Mnaouar, BP 1505, Bir El Djir 31000, Oran, Algeria, e-mail: blouhitayeb1984@gmail.com
  • Mohamed FERHAT Faculty of Mathematics and Computer Science, Department of Mathematics, University of Science and Technology, Mohamed-Boudiaf El Mnaouar, BP 1505, Bir El Djir 31000, Oran, Algeria, e-mail: ferhat22@hotmail.fr
  • Safia BENMANSOUR 01, Rue Barka Ahmed Bouhannak Imama Pr´es du Commissariat des 400 Logements de Bouhannak, Tlemcen 13000 Algeria, e-mail: safiabenmansour@hotmail.fr

DOI:

https://doi.org/10.24193/subbmath.2022.4.07

Keywords:

Sweeping process, evolution inclusion, perturbation, normal cone, fixed point.

Abstract

This paper is devoted to the study of a convex stochastic sweeping process with fractional Brownian by time delay. The approach is based on discretizing stochastic functional differential inclusions.

Mathematics Subject Classification (2010): 34A37, 34K45, 60H99, 60H05, 65C30, 47H10.

Received 28 November 2019; Accepted 17 January 2020.

References

Bharucha-Reid, A.T., Random Integral Equations, Academic Press, New York, 1972. [2] Castaing, C., Sur un nouvelle classe d’equation d’evolution dans les espaces de Hilbert, expose no 10, Seminaire d’analyse convexe, University of Montpellier, 24 pages, 1983.

Da Prato, G., Zabczyk, J., Stochastic Equations in Infinite Dimensions, Cambridge Univ Press, Cambridge, 1992.

Gard, T.C., Introduction to Stochastic Differential Equations, Marcel Dekker, New York, 1988.

Gavioli, A., Approximation from the exterior of a multifunction and its applications in the ”sweeping process”, J. Diff. Equations, 92(1992), 121-124.

Mao, X., Stochastic Differential Equations and Applications, Harwood, Chichester, 1997. [7] Moreau, J.J., Rale par un convexe variable, (premiere partie), expose no 15, Seminaire d’analyse convexe, University of Montpellier, 43 pages, 1971.

Moreau, J.J., Probleme d’evolution associ´e a un convexe mobile d’un espace hilbertien, C. R. Acad. Sci. Paris, Serie A-B, (1973), 791-794.

Øksendal, B., Stochastic Differential Equations: An Introduction with Applications, (Fourth Edition), Springer-Verlag, Berlin, 1995.

Sobczyk, H., Stochastic Differential Equations with Applications to Physics and Engineering, Kluwer Academic Publishers, London, 1991.

Tsokos, C.P., Padgett, W.J., Random Integral Equations with Applications to Life Sciences and Engineering, Academic Press, New York, 1974.

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Published

2022-12-02

How to Cite

BLOUHI, T., FERHAT, M., & BENMANSOUR, S. (2022). Existence for stochastic sweeping process with fractional Brownian motion. Studia Universitatis Babeș-Bolyai Mathematica, 67(4), 749–771. https://doi.org/10.24193/subbmath.2022.4.07

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