与分数Brown运动相比，分数Levy过程在刻画噪声的长相依性质的同时，在考虑噪声的分布方面有更多的灵活性。分数Levy过程代表着受到跳跃的长相依型随机因素干扰的系统，从而可以更好地刻画金融和随机网络等领域具有较高波动率的随机现象，因此受到了广泛关注。关于分数Levy过程的随机积分理论及其驱动的随机微分方程成为近几年来很多学者关注的问题。. 本项目的主要目标是用白噪声方法构造多参数分数Levy随机场的随机积分，在此基础上，用白噪声方法研究由分数Levy噪声驱动的随机Poisson方程、随机Schrodinger方程和随机热方程在随机分布函数空间的解及解的性质。本项目的成功实施不仅在理论上使得分数Levy过程的理论体系更加完备，而且可以更好地推动它的应用。

While capturing memory effects in a similar fashion as a fractional Brownian motion (FBM) does, the fractional Levy process (FLP) built by the same convolution as FBM with a Levy process provides more flexibility concerning the distribution of the noise. A FLP represents the system impacted by the jump and long-range dependent noise,which makes it can model noises in finance and network traffic. The stochastic integration of the fractional Levy processes and the stochastic differential equation driven by them are of great interest.. The aim of this proposal is to build the stochastic integral for multi-parameter fractional Levy random field and then to investigate the solutions to the stochastic Poisson equation, the stochastic Schrodinger equation and stochastic heat equation driven by fractional Levy noises in the space of stochastic distribution functions by white noise approach. The successful implement of this proposal can not only make the theory of the fractional Levy process more complete, but also make the process more applicable.