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Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay

  • Hussein K. Asker EMAIL logo
Published/Copyright: November 17, 2020
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Abstract

In this work, neutral stochastic functional differential equations with infinite delay (NSFD-EwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space Cr under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the L2 and exponential estimates of NSFDEwID have been studied.

Acknowledgement

The author would like to thank Dr Jianhai Bao for his encouragement and kindly advice throughout this work, as well as Professor Chenggui Yuan for his supervision and remarks. This research was supported by Kufa University and the Iraqi Ministry of Higher Education and Scientific Research.

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Received: 2020-03-15
Accepted: 2020-05-06
Published Online: 2020-11-17
Published in Print: 2020-11-25

© 2020 Walter De Gruyter GmbH, Berlin/Boston

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