Quantum and non-causal stochastic calculus
Quantum and non-causal stochastic calculus
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量子和非因果随机微积分
DOI：
10.1007/bf01199312
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发表时间：
1993
影响因子：
2
通讯作者：
J. Lindsay
中科院分区：
文献类型：
--
作者：
J. Lindsay
由哈德逊和Parthasarathy发起的量子随机演算，以及由Hitsuda和Skorohod的论文发起的非因果随机演算，是伊藤演算的两个有力的扩展，目前正在得到深入的发展。前者提供了薛定谔方程的量子概率扩展，使量子动力学半群的马尔可夫过程的建设。后者允许随机微分方程的治疗，其中涉及预期的未来。在本文中，这些理论之间的密切关系显示，和非因果量子随机演算，已经在物理学的需求，描述。
The quantum stochastic calculus initiated by Hudson and Parthasarathy, and the non-causal stochastic calculus originating with the papers of Hitsuda and Skorohod, are two potent extensions of the Itô calculus, currently enjoying intensive development. The former provides a quantum probabilistic extension of Schrödinger's equation, enabling the construction of a Markov process for a quantum dynamical semigroup. The latter allows the treatment of stochastic differential equations which involve terms which anticipate the future. In this paper the close relationship between these theories is displayed, and a noncausal quantum stochastic calculus, already in demand from physics, is described.