The existence and asymptotic behaviour of energy solutions to stochastic age-dependent population equations driven by Levy processes

In this paper, we introduce a class of stochastic age-dependent population equations driven by Levy processes. Existence and uniqueness of energy solutions for stochastic age-dependent population dynamic system are proved under Lipschitz condition in Hilbert space. The moment boundedness of the approximate solution by the Galerkin method is considered. We discuss by using the energy equality the exponential stability theorems of the energy solution to stochastic age-dependent population equations.

[1]  Li Ronghua,et al.  Convergence of numerical solutions to stochastic age-dependent population equations , 2006 .

[2]  B. Øksendal.  Stochastic differential equations : an introduction with applications , 1987 .

[3]  X. Mao,et al.  Competitive Lotka–Volterra population dynamics with jumps , 2011, 1102.2163.

[4]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[5]  C. Yuan,et al.  Stochastic Population Dynamics Driven by Levy Noise , 2011, 1105.1174.

[6]  A. Rathinasamy,et al.  Split-step θ-methods for stochastic age-dependent population equations with Markovian switching , 2012 .

[7]  Ke Wang,et al.  Dynamics of a Leslie-Gower Holling-type II predator-prey system with Lévy jumps , 2013 .

[8]  The existence and asymptotic behaviour of energy solutions to stochastic 2D functional Navier–Stokes equations driven by Levy processes , 2012 .

[9]  Jiye Zhang,et al.  Absolute stability analysis in cellular neural networks with variable delays and unbounded delay , 2004 .

[10]  Takeshi Taniguchi,et al.  The exponential stability for stochastic delay partial differential equations , 2007 .

[11]  Zhang Qi-min,et al.  Existence, uniqueness and exponential stability for stochastic age-dependent population , 2004 .

[12]  V. Mandrekar,et al.  Existence and uniqueness of path wise solutions for stochastic integral equations driven by Lévy noise on separable Banach spaces , 2006 .

[13]  Chenggui Yuan,et al.  Exponential stability of energy solutions to stochastic partial differential equations with variable delays and jumps , 2010 .

[14]  E. Hausenblas.  Existence, Uniqueness and Regularity of Parabolic SPDEs Driven by Poisson Random Measure , 2005 .

[15]  Mingzhu Liu,et al.  Convergence and stability of the semi-implicit Euler method for a linear stochastic differential delay equation , 2004 .

[16]  Xicheng Zhang,et al.  SUCCESSIVE APPROXIMATIONS OF INFINITE DIMENSIONAL SDES WITH JUMP , 2005 .

[17]  Qi-min Zhang,et al.  Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion , 2012 .