Turkish Journal of Mathematics

Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(W,C_h)
Haibo BAO
Department of Mathematics and Physics,
Hohai University, Nanjing,
210098, Jiangsu-CHINA
e-mail: hbbao@hhu.edu.cn

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(W,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(W,C_h) \to L^p(W,Rⁿ), g:R⁺\times L^p(W,C_h) \to L^p(W,L(R^m, Rⁿ)), G: L^p(W,C_h) \to L^p(W,Rⁿ), p>2,\, and B(t) is a given m-dimensional Brownian motion.

Key Words: Neutral stochastic functional differential equations; existence; uniqueness; infinite delay.

Turk. J. Math., 34, (2010), 45-58.
Full text: pdf
Other articles published in the same issue: Turk. J. Math.,vol.34,iss.1.