Local Existence of Solution to a Class of Stochastic Differential Equations with Finite Delay in Hilbert Spaces

Abstract

In this paper, we present a local Lipchitz condition for the local existence of solution to a class of stochastic differential equations with finite delay in a real separable Hilbert space which has the following form:

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L. Minh, H. Nam and N. Thuan, "Local Existence of Solution to a Class of Stochastic Differential Equations with Finite Delay in Hilbert Spaces," Applied Mathematics, Vol. 4 No. 1, 2013, pp. 97-101. doi: 10.4236/am.2013.41017.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] P. H. Bezandry and T. Diagana, “Almost Periodic Stochastic Processes,” Springer, Berlin, 2011. doi:10.1007/978-1-4419-9476-9
[2] N. M. Chuong and N. X. Thuan, “The Surjectivity of Semiregular Maximal Monotone Random Mappings,” Random Operators and Stochastic Equations, Vol. 10, No. 1, 2002, pp. 13-24.
[3] N. M. Chuong and N. X. Thuan, “Random Equations for Weakly Semi-Monotone Operators of Type (S) and Semi J-Monotone Operators of Type (J-S),” Random Operators and Stochastic Equations, Vol. 10, No. 2, 2002, pp. 123-132.
[4] N. M. Chuong and N. X. Thuan, “Random Equations for Semi H-Monotone Operators,” Random Operators and Stochastic Equations, Vol. 10, No. 4, 2002, pp. 1-8.
[5] N. M. Chuong and N. X. Thuan, “Random Nonlinear Variational Inequalities for Mappings of Monotone Type in Banach Spaces,” Stochastic Analysis and Applications, Vol. 24, No. 3, 2006, pp. 489-499. doi:10.1080/SAP-200064451
[6] N. M. Chuong and N. X. Thuan, “Random Fixed Point Theorems for Multivalued Nonlinear Mappings,” Random Operators and Stochastic Equations, Vol. 9, No. 3, 2001, pp. 1-10.
[7] L. Gawarecki and V. Mandrekar, “Stochastic Differential Equations in Infinite Dimensions,” Springer, Berlin, 2011. doi:10.1007/978-3-642-16194-0
[8] G. Da Prato and L. Tubaro, “Stochastic Partial Differential Equations and Applications, VII,” Chapman & Hall/ CRC, New York, 2006.

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