Abstract
The main aim of this paper is to discuss the existence and uniqueness of solution of the neutral stochastic functional differential infinite delay equations under a non-Lipschitz condition and a weakened linear growth condition. Furthermore, an estimate for the error between approximate solution and accurate solution is given. MSC:60H05, 60H10.
Highlights
Stochastic differential equations (SDEs) are well known to model problems from many areas of science and engineering
Kolmanovskii and Myshkis [ ] introduced the following neutral stochastic differential equations with finite delay: d x(t) – G(xt) = f (t, xt) dt + g(t, xt) dB(t) which could be used in chemical engineering and aeroelasticity
Motivated by [ ], one of the objectives of this paper is to get one proof to the existence and uniqueness theorem for given neutral stochastic functional differential equations (SFDEs), which contains an improved condition given in [ ]
Summary
Stochastic differential equations (SDEs) are well known to model problems from many areas of science and engineering. Motivated by [ ], one of the objectives of this paper is to get one proof to the existence and uniqueness theorem for given neutral SFDEs, which contains an improved condition given in [ ]. The other objective of this paper is to estimate on how fast the Picard iterations xn(t) converge the unique solution x(t) of the neutral SFDEs. 2 Preliminary and notations Rd-value stochastic process x(t) defined on –∞ < t ≤ T is called the solution of
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