Abstract: For a population dynamics system, the influences of the stochastic external environment upon the system are not considered in ordinary age-dependent system models. When the system is perturbed by a random external environment, a class of stochastic age-dependent population dynamics system with diffusion was proposed. The existence and uniqueness of solution to a stochastic age-dependent population dynamics system with diffusion were discussed in Hilbert space by using the Burkholder-Davis-Gundy inequality, Gronwall lemma and Klmogrorov inequality. The result was illustrated by a specific example.

Key words: Burkholder-Davis-Gundy inequality , It formula, stochastic population system