Mean Square Summability of Solution of Stochastic Difference Second-Kind Volterra Equation with Small Nonlinearity

作者: Beatrice Paternoster , Leonid Shaikhet

DOI: 10.1155/2007/65012

关键词: First-order partial differential equationIntegral equationVolterra integral equationStochastic partial differential equationDifferential equationPartial differential equationMathematicsStochastic differential equationFunctional equationMathematical analysis

摘要: Stochastic difference second-kind Volterra equation with continuous time and small nonlinearity is considered. Via the general method of Lyapunov functionals construction, sufficient conditions for uniform mean square summability solution considered are obtained.

参考文章(15)
I. I. Gikhman, Theory of stochastic processes John Wiley. ,(1974)
Vito Volterra, Marcel Brelot, Leçons sur la théorie mathématique de la lutte pour la vie Éditions Jacques Gabay. ,(1931)
Ch G Philos, IK Purnaras, An asymptotic result for some delay difference equations with continuous variable Advances in Difference Equations. ,vol. 2004, pp. 679264- ,(2004) , 10.1155/S1687183904310058
V. Kolmanovskii, L. Shaikhet, Construction of lyapunov functionals for stochastic hereditary systems: a survey of some recent results Mathematical and Computer Modelling. ,vol. 36, pp. 691- 716 ,(2002) , 10.1016/S0895-7177(02)00168-1
V. Kolmanovskii, L. Shaikhet, Some peculiarities of the general method of Lyapunov functionals construction Applied Mathematics Letters. ,vol. 15, pp. 355- 360 ,(2002) , 10.1016/S0893-9659(01)00143-4
Leonid E. Shaikhet, Jason A. Roberts, Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations Advances in Difference Equations. ,vol. 2006, pp. 073897- ,(2006) , 10.1155/ADE/2006/73897
B Paternoster, L Shaikhet, Application of the general method of Lyapunov functionals construction for difference Volterra equations Computers & Mathematics with Applications. ,vol. 47, pp. 1165- 1176 ,(2004) , 10.1016/S0898-1221(04)90111-3
V.B. Kolmanovskii, The stability of certain discrete-time volterra equations Journal of Applied Mathematics and Mechanics. ,vol. 63, pp. 537- 543 ,(1999) , 10.1016/S0021-8928(99)00068-4