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A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions

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  • Ren, Yong
  • Hou, Tingting
  • Sakthivel, R.
  • Cheng, Xing

Abstract

In this note, we aim to study a class of second-order non-autonomous neutral stochastic evolution equations with infinite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion with Hurst parameter H∈(1/2,1), in which the initial value belongs to the abstract space B. We establish the existence and uniqueness of mild solutions for this kind of equations under some Carathéodory conditions by means of the successive approximation. The obtained result extends some well-known results. An example is proposed to illustrate the theory.

Suggested Citation

  • Ren, Yong & Hou, Tingting & Sakthivel, R. & Cheng, Xing, 2014. "A note on the second-order non-autonomous neutral stochastic evolution equations with infinite delay under Carathéodory conditions," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 658-665.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:658-665
    DOI: 10.1016/j.amc.2014.01.091
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    References listed on IDEAS

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    1. Boufoussi, Brahim & Hajji, Salah, 2012. "Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1549-1558.
    2. Mark A. McKibben, 2004. "Second-order neutral stochastic evolution equations with heredity," International Journal of Stochastic Analysis, Hindawi, vol. 2004, pages 1-16, January.
    3. P. Balasubramaniam & P. Muthukumar, 2009. "Approximate Controllability of Second-Order Stochastic Distributed Implicit Functional Differential Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 225-244, November.
    4. Y. Ren & D. D. Sun, 2010. "Second-order Neutral Stochastic Evolution Equations with Infinite Delay under Carathéodory Conditions," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 569-582, December.
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