Stabilization of Volterra equations by noise

[摘要] The paper studies the stability of an autonomous convolutionItô-Volterra equation where the linear diffusion termdepends on the current value of the state only, and the memory ofthe past fades exponentially fast. It is shown that the presenceof noise can stabilize an equilibrium solution which is unstablein the absence of this noise.

[学科分类] 应用数学