Electronic Communications in Probability

Mild Solutions of Quantum Stochastic Differential Equations

Franco Fagnola and Stephen Wills

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Abstract

We introduce the concept of a mild solution for the right Hudson-Parthasarathy quantum stochastic differential equation, prove existence and uniqueness results, and show the correspondence between our definition and similar ideas in the theory of classical stochastic differential equations. The conditions that a process must satisfy in order for it to be a mild solution are shown to be strictly weaker than those for it to be a strong solution by exhibiting a class of coefficient matrices for which a mild unitary solution can be found, but for which no strong solution exists.

Article information

Source
Electron. Commun. Probab., Volume 5 (2000), paper no. 17, 158-171.

Dates
Accepted: 30 November 2000
First available in Project Euclid: 2 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456943510

Digital Object Identifier
doi:10.1214/ECP.v5-1029

Mathematical Reviews number (MathSciNet)
MR1800118

Zentralblatt MATH identifier
0967.60064

Subjects
Primary: 81S25: Quantum stochastic calculus

Keywords
Quantum stochastic stochastic differential equation mild solution

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Fagnola, Franco; Wills, Stephen. Mild Solutions of Quantum Stochastic Differential Equations. Electron. Commun. Probab. 5 (2000), paper no. 17, 158--171. doi:10.1214/ECP.v5-1029. https://projecteuclid.org/euclid.ecp/1456943510


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The Institute of Mathematical Statistics and the Bernoulli Society

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