Existence for stochastic sweeping process with fractional Brownian motion
DOI:
https://doi.org/10.24193/subbmath.2022.4.07Keywords:
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 dierential inclusions..
References
C. Castaing, M. Valadier, Convex Analysis and Measurable Multifunctions,in: Lec-
ture Notes in Mathematics, vol. 580.
C. P. Tsokos, W.J. Padgett, Random Integral Equations with Applications to Life
Sciences and Engineering, Academic Press, New York, 1974.
D. Nualart, The Malliavin Calculus and Related Topics, second edition, Springer-
Verlag, Berlin, 2006.
F. H. Clarke, Yu. S. Ledyaev, R. J . Sten and P. R.Wolenski, Nonsmooth Analysis
and Control Theory, Springer, New York, 1998.
F. H. Clarke, Nonsmooth Analysis, Wiley-Interscience, New York, 1988.
Clarke, F. H., Ledyaev, Yu. S., Stern, R. J. and Wolenski, P. R.: Nonsmooth
Analysis and Control Theory, Springer, New York, 1998.
G. Da Prato and J. Zabczyk, Stochastic Equations in Innite Dimensions, Cam-
bridge University Press, Cambridge, 1992.
H. Sobczyk, Stochastic Dierential Equations with Applications to Physics and
Engineering, Kluwer Academic Publishers, London, 1991.
J.J. Moreau, Evolution problem associated with a moving convex set in a Hilbert
space, J. Dierential Equations 26 347374.
J. J. Moreau, Rale par un convexe variable (premiere partie), expose no 15. Sem-
inaire d'analyse convexe, University of Montpellier, 43 pages, 1971.
J. J. Moreau. Probleme d'evolution associ'e a un convexe mobile d'un espace
hilbertien. C. R. Acad. Sc. Paris, Serie A-B, (1973), 791-794.
J.P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhauser, Boston, 1990.
K. Deimling, Multi-valued Dierential Equations, De Gruyter, Berlin, New York,
L. Gorniewicz, Topological Fixed Point Theory of Multi-Valued Mappings, in:
Mathematics and its Applications, vol. 495, Kluwer Academic Publishers, Dor-
drecht, 1999.
S. Djebali, L. Gorniewicz, and A. Ouahab, First order periodic impulsive semi-
linear dierential inclusions: existence and structure of solution sets, Math. and
Comput. Mod., 52 (2010), 683{714.
T. Blouhi, T. Caraballo, A. Ouahab, Existence and stability results for semilinear
systems of impulsive stochastic dierential equations with fractional Brownian
motion, Stoch. Anal. Appl.5 (2016),792834.
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