Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(\Omega,C_h)

Authors

HAIBO BAO

DOI

10.3906/mat-0806-3

Abstract

In this paper, we shall consider the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(\Omega,C_h) space: d[x(t)-G(x_t)]=f(t,x_t)dt+g(t,x_t)dB(t), where we assume f:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,R^n), g:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,L(R^m, R^n)), G: L^p(\Omega,C_h) \to L^p(\Omega,R^n), p>2,\, and B(t) is a given m-dimensional Brownian motion.

Keywords

Neutral stochastic functional differential equations; existence; uniqueness; infinite delay.

First Page

45

Last Page

58

Recommended Citation

BAO, HAIBO (2010) "Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(\Omega,C_h)," Turkish Journal of Mathematics: Vol. 34: No. 1, Article 5. https://doi.org/10.3906/mat-0806-3
Available at: https://journals.tubitak.gov.tr/math/vol34/iss1/5