Existence and Uniqueness Results for Neutral SDEs in Hilbert Spaces

Abstract In this paper using a Picard type approximation, we present the existence and uniqueness theorems for mild solutions of the semilinear neutral SDEs in Hilbert spaces whose coefficients satisfy non-Lipschitz condition.

[1]  Toshio Yamada,et al.  On the successive approximation of solutions of stochastic differential equations , 1981 .

[2]  On existence and uniqueness of solution of stochastic differential equations with heredity , 1984 .

[3]  Successive approximations for solutions of stochastic integral equations of Volterra type , 1984 .

[4]  T. Taniguchi.  Successive Approximations to Solutions of Stochastic Differential Equations , 1992 .

[5]  B. Z. Zangeneh.  Semilinear stochastic evolution equations with monotone nonlinearities , 1995 .

[6]  Xiao Xin Liao.  Exponential Stability in Mean Square of Neutral Stochastic Differential Difference Equations , 1995 .

[7]  X. Mao.  RAZUMIKHIN-TYPE THEOREMS ON EXPONENTIAL STABILITY OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS∗ , 1997 .

[8]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[9]  Yi Shen,et al.  Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations , 1999 .

[10]  Kai Liu,et al.  On the exponential stability in mean square of neutral stochastic functional differential equations , 1999 .

[11]  X. Mao,et al.  Asymptotic properties of neutral stochastic differential delay equations , 2000 .

[12]  T. E. Govindan,et al.  Stability of Mild Solutions of Stochastic Evolution Equations with Variable Delay , 2001 .

[13]  D. Barbu,et al.  Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients , 2002 .

[14]  Y. El Boukfaoui,et al.  Remarks on the existence and approximation for semilinear stochastic differential equations in Hilbert spaces , 2002 .

[15]  Nazim I. Mahmudov,et al.  On controllability of semilinear stochastic systems in Hilbert spaces , 2002 .

[16]  Nazim I. Mahmudov,et al.  Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces , 2003, SIAM J. Control. Optim..

[17]  A. I. Matasov,et al.  Neutral Stochastic Differential Delay Equations with Markovian Switching , 2003 .

[18]  M. McKibben.  Second-order neutral stochastic evolution equations with heredity , 2004 .

[19]  D. Vinayagam,et al.  Existence of Solutions of Nonlinear Neutral Stochastic Differential Inclusions in a Hilbert Space , 2005 .

[20]  T. Kurtz,et al.  Stochastic equations in infinite dimensions , 2006 .

[21]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .