Successive Approximation of Neutral Functional Stochastic Differential Equations in Hilbert Spaces

Brahim Boufoussi[1]; Salah Hajji[1]

  • [1] Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco

Annales mathématiques Blaise Pascal (2010)

  • Volume: 17, Issue: 1, page 183-197
  • ISSN: 1259-1734

Abstract

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By using successive approximation, we prove existence and uniqueness result for a class of neutral functional stochastic differential equations in Hilbert spaces with non-Lipschitzian coefficients

How to cite

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Boufoussi, Brahim, and Hajji, Salah. "Successive Approximation of Neutral Functional Stochastic Differential Equations in Hilbert Spaces." Annales mathématiques Blaise Pascal 17.1 (2010): 183-197. <http://eudml.org/doc/116348>.

@article{Boufoussi2010,
abstract = {By using successive approximation, we prove existence and uniqueness result for a class of neutral functional stochastic differential equations in Hilbert spaces with non-Lipschitzian coefficients},
affiliation = {Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco; Department of Mathematics Cadi Ayyad University Semlalia Faculty of Sciences 2390 Marrakesh Morocco},
author = {Boufoussi, Brahim, Hajji, Salah},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Semigroup of bounded linear operator; Fractional powers of closed operators; Successive approximation; Mild solution; Cylindrical $Q$-Wiener process; semigroup of bounded linear operator; fractional powers of closed operators; successive approximation; mild solution; cylindrical -Wiener process},
language = {eng},
month = {1},
number = {1},
pages = {183-197},
publisher = {Annales mathématiques Blaise Pascal},
title = {Successive Approximation of Neutral Functional Stochastic Differential Equations in Hilbert Spaces},
url = {http://eudml.org/doc/116348},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Boufoussi, Brahim
AU - Hajji, Salah
TI - Successive Approximation of Neutral Functional Stochastic Differential Equations in Hilbert Spaces
JO - Annales mathématiques Blaise Pascal
DA - 2010/1//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 1
SP - 183
EP - 197
AB - By using successive approximation, we prove existence and uniqueness result for a class of neutral functional stochastic differential equations in Hilbert spaces with non-Lipschitzian coefficients
LA - eng
KW - Semigroup of bounded linear operator; Fractional powers of closed operators; Successive approximation; Mild solution; Cylindrical $Q$-Wiener process; semigroup of bounded linear operator; fractional powers of closed operators; successive approximation; mild solution; cylindrical -Wiener process
UR - http://eudml.org/doc/116348
ER -

References

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  10. K. Liu, X. Xia, On the exponential stability in mean square of neutral stochastic functional differential equations, Systems Control Lett 37(4) (1999), 207-215 Zbl0948.93060MR1751250
  11. N.I. Mahmudov, Existence and uniqueness results for neutral SDEs in Hilbert spaces, Stochastic Analysis and Applications 24 (2006), 79-95 Zbl1110.60063MR2198538
  12. X. Mao, Exponential stability in mean square of neutral stochastic differential functional equations, Systems and Control Letters 26 (1995), 245-251 Zbl0877.93133MR1360915
  13. X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional-differential equations, SIAM J. Math. Anal 28(2) (1997), 389-401 Zbl0876.60047MR1434042
  14. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, (1983), Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York Zbl0516.47023MR710486
  15. J. Wu, Theory and Applications of Partial Functional Differential Equations, (1996), Applied Mathematical Sciences Volume 119, Springer-Verlag, New York Zbl0870.35116MR1415838

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