.
.
"On dissipative stochastic equations in a Hilbert space" .
.
.
.
"A. S." .
_:N51c411e41b0845e18a7c824e8ab2df67 .
_:Nca14069a1d0347dcafca948520221c3e .
.
"1432-2064" .
.
"Probability Theory and Related Fields" .
.
.
.
.
"Mathematical Sciences" .
_:N51c411e41b0845e18a7c824e8ab2df67 .
_:N95e4d0c63e884aadaa338365f3ad8e6c "readcube_id" .
.
_:N95e4d0c63e884aadaa338365f3ad8e6c "c36797742152d47d6926add45047e1863498d2fe545ca5544e22a06f39cd8851" .
_:N72774ab629d14b19806fdfc3b0ea8512 .
.
.
_:Nca14069a1d0347dcafca948520221c3e "pub.1041019695" .
.
_:N72774ab629d14b19806fdfc3b0ea8512 .
.
.
"Holevo" .
"Steklov Mathematical Institute" .
.
.
.
.
"research_article" .
_:Nca14069a1d0347dcafca948520221c3e .
.
.
.
"1996-12-01" .
"Applied Mathematics" .
.
"false"^^ .
_:N1bbc3c0bc37d4200bb2e12287a8bbcb5 "104" .
_:Nda3fb184958a469e810b985398305425 .
_:N727156bb15554457b9cd3a8040ac5f5f .
.
"2019-04-11T13:27" .
.
.
"https://scigraph.springernature.com/explorer/license/" .
.
"en" .
.
.
.
_:N727156bb15554457b9cd3a8040ac5f5f "Springer Nature - SN SciGraph project" .
.
.
"0178-8051" .
.
_:Nda3fb184958a469e810b985398305425 "10.1007/bf01198163" .
.
_:N727156bb15554457b9cd3a8040ac5f5f .
.
"articles" .
.
.
.
.
.
_:N1bbc3c0bc37d4200bb2e12287a8bbcb5 .
.
.
_:N51c411e41b0845e18a7c824e8ab2df67 "4" .
"http://link.springer.com/10.1007/BF01198163" .
.
_:Nca14069a1d0347dcafca948520221c3e "dimensions_id" .
_:Nda3fb184958a469e810b985398305425 .
_:N72774ab629d14b19806fdfc3b0ea8512 .
.
"A general existence and uniqueness theorem for solutions of linear dissipative stochastic differential equation in a Hilbert space is proved. The dual equation is introduced and the duality relation is established. Proofs take inspirations from quantum stochastic calculus, however without using it. Solutions of both equations provide classical stochastic representation for a quantum dynamical semigroup, describing quantum Markovian evolution. The problem of the mean-square norm conservation, closely related to the unitality (non-explosion) of the quantum dynamical semigroup, is considered and a hyperdissipativity condition, ensuring such conservation, is discussed. Comments are given on the existence of solutions of a nonlinear stochastic differential equation, introduced and discussed recently in physical literature in connection with continuous quantum measurement processes." .
"1996-12" .
.
.
.
.
.
.
.
_:N95e4d0c63e884aadaa338365f3ad8e6c .
.
.
"483-500" .
_:Nda3fb184958a469e810b985398305425 "doi" .
.
"Steklov Mathematical Institute, Vavilova 42, 117966, Moscow, Russia" .
.
.
_:N95e4d0c63e884aadaa338365f3ad8e6c .
_:N1bbc3c0bc37d4200bb2e12287a8bbcb5