Stochastic Schr dinger equation driven by pure jump Lévy white noise

DOI：10.7511/dllgxb200805027

 作者 单位 冯敬海,王岩,冯恩民

给出了由纯跳Lévy白噪声驱动的随机薛定谔方程的白噪声解法．方程的位势由纯跳Lévy白噪声过程的Wick幂来表示，在实际应用中代表随机因素是跳跃的物理系统．此方法将 (S) -1 分布空间的特征定理作为理论基础，利用Hermite变换将随机薛定谔方程转化为非随机的普通方程，在Feynmann-Kac公式的帮助下，得到这个非随机方程的解，最后使用\{Hermite\}反变换将此解转换为分布空间的一个 (S) -1 过程，这个过程即为原随机薛定谔方程的解．进一步可以得到 经过一定条件的限制，这个解在弱分布的意义下，属于 L 1(υ) 空间．

The white noise approach for stochastic Schr dinger equation (SSE) driven by pure jump Lévy white noise is presented. The potential of the SSE is proportional to the Wick exponential of pure jump Lévy white noise, which describes the physical system with jump. The white noise approach is based on \%(S) -1 \%-characterization theorem. The SSE is firstly reduced to the ordinary non-random Schr dinger equation (OSE) by Hermite transform, which can be solved by Feynmann-Kac formula. Then the solution of the SSE is obtained by (S) -1 -characterization theorem, converting the solution of the OSE to a (S) -1 -process . Furthermore, the solution is in L 1(υ) in sense of weak distribution under some certain conditions.