Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 5 (2000), paper no. 17, 158-171.
Mild Solutions of Quantum Stochastic Differential Equations
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.
Electron. Commun. Probab., Volume 5 (2000), paper no. 17, 158-171.
Accepted: 30 November 2000
First available in Project Euclid: 2 March 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 81S25: Quantum stochastic calculus
This work is licensed under aCreative Commons Attribution 3.0 License.
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