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On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States

Russian Journal of Mathematical Physics. 2025. Vol. 32. P. 510–529.
Kolokoltsov V.

Quantum filtering equations for mixed states were developed in the eighties of the last
century. Since then, the problem of constructing a rigorous mathematical theory for these equations
in the basic infinite-dimensional settings has been a challenging open mathematical problem. In a
previous paper, the author developed the theory of these equations in the case of bounded coupling
operators, including a new version that arises as the law of large numbers for interacting particles
under continuous observation and thus leading to the theory of quantum mean field games. In this
paper, the main body of these results is extended to the basic cases of unbounded coupling operators.

Research target: Mathematics Physics
Language: English
Full text
DOI
Text on another site
Keywords: quantum filteringstochastic Lindblad equationsmixed statesstochastic equations with singular coefficients
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