QUANTUM AND NONCAUSAL STOCHASTIC CALCULUS

• 成果类型: Article
• 署名作者: LINDSAY, JM
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01199312
• 发表日期: 1993
• 页码: 65-80
• 关键词: malliavin calculus; fock space; integration; evolutions; FORMULA

摘要

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 Ito calculus, currently enjoying intensive development. The former provides a quantum probabilistic extension of Schrodinger'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 non-causal quantum stochastic calculus, already in demand from physics, is described.