一般类型随机Volterra积分方程解的存在唯一性

The existence and uniqueness of solutions to stochastic Volterra equations with general type

用随机Volterra方程刻画的数学模型,常见于许多经济、生态和化学等问题中,具有广泛的实际应用前景。给出随机Volterra方程解的定义及解的存在唯一性定理,应用压缩映像原理证明了一般类型随机Volterra方程的特殊形式的方程解的存在唯一性,随后给出并证明了一般类型随机Volterra方程的解的存在唯一性。

Models described by SVEs （ stochastic Volterra equations） are often met in many problems of economy, ecology and chemistry. Its importance consist in not only it exists in many fields, but also has broad prospects for the practical application. The definition and theorem of existence and uniqueness for the solutions to SVEs are first presented. The existence and uniqueness of solutions to a special type of GSVEs （ stochastic Voherra equations with general type） are investigated by applying the principle of contraction mapping. Based on this, the theorem of existence and uniqueness of the solutions to GSVEs are presented.