用算子理论推广Wiener积分
An extension of Wiener integration with the use of operator theory
摘要：
利用Hilbert空间的张量积和算子理论中的对角化方法，导出了一类随机积分的逼近公式.进一步，我们建立了这些随机积分的广义傅立叶展开。在我们的扩展中，我们规避了由于Wiener和Ito而更广泛使用的随机积分的一些限制，即，关于布朗运动随机积分最后，我们讨论了这两种方法之间的联系，以及先验估计和应用。
英文摘要：
With the use of tensor product of Hilbert space, and a diagonalization procedure from operator theory, we derive an approximation formula for a general class of stochastic integrals. Further we establish a generalized Fourier expansion for these stochastic integrals. In our extension, we circumvent some of the limitations of the more widely used stochastic integral due to Wiener and Ito, i.e., stochastic integration with respect to Brownian motion. Finally we discuss the connection between the two approaches, as well as a priori estimates and applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
