Results 141 to 150 of about 159 (158)
Some of the next articles are maybe not open access.
Wick Calculus of Generalized Operators and its Applications to Quantum Stochastic Calculus
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 1998A nonlinear and stochastic analysis of free Bose field is established in the framework of white noise calculus. Wick algebra structure is introduced in the space of generalized operators generated by quantum white noise, some fundamental properties of the calculus based on the Wick algebra are investigated.
Huang, Zhiyuan, Luo, Shunlong
openaire +2 more sources
Quantum and non-causal stochastic calculus
Probability Theory and Related Fields, 1993The quantum stochastic calculus initiated by \textit{R. L. Hudson} and \textit{K. R. Parthasarathy} [Commun. Math. Phys. 93, 301-323 (1984; Zbl 0546.60058)], and the noncausal stochastic calculus originating with the papers of \textit{M. Hitsuda} [Proc. 2nd Japan-USSR Symp. Probab. Theory 2, 111-114 (1972)] and \textit{A. V.
openaire +1 more source
1990
We show that every norm continuous one-parameter semigroup (ℐt: t ∈ ℝ+) of unital ultraweakly continuous completely positive maps on the algebra ℬ(ℋ0) of bounded operators on the separable infinite dimensional Hilbert space ℋ0 can be expressed as Open image in new window where (j t : t ∈ ℝ+) is a quantum diffusion over ℬ(ℋ0) constructed using only ...
R L Hudson, P Shepperson
openaire +1 more source
We show that every norm continuous one-parameter semigroup (ℐt: t ∈ ℝ+) of unital ultraweakly continuous completely positive maps on the algebra ℬ(ℋ0) of bounded operators on the separable infinite dimensional Hilbert space ℋ0 can be expressed as Open image in new window where (j t : t ∈ ℝ+) is a quantum diffusion over ℬ(ℋ0) constructed using only ...
R L Hudson, P Shepperson
openaire +1 more source
2012
Martingales are fundamental stochastic process used to model the concept of fair game. They have a multitude of applications in the real world that include, random walks, Brownian motion, gamblers fortunes and survival analysis, Just as commutative integration theory may be realised as a special case of the more general non-commutative theory for ...
openaire +1 more source
Martingales are fundamental stochastic process used to model the concept of fair game. They have a multitude of applications in the real world that include, random walks, Brownian motion, gamblers fortunes and survival analysis, Just as commutative integration theory may be realised as a special case of the more general non-commutative theory for ...
openaire +1 more source
Continual Measurements in Quantum Mechanics and Quantum Stochastic Calculus
20061 Introduction 31.1 Three approaches to continual measurements 31.2 Quantum stochastic calculus and quantum optics 31.3 Some notations: operator spaces 42 Unitary evolution and states 52.1 Quantum stochastic calculus 5The Fock space 5The Weyl operators and the Bose fields 6Quantum stochastic integrals 92.2 The unitary system–field ...
openaire +2 more sources
Quantum Stochastic Calculus and Applications — A Review
1998It has been a little more than a decade since this subject, as it is understood today, came into being with the seminal paper of Hudson and Parthasarathy [1]. Since then the subject has seen rapid development and many of these can be found in the monographs of Parthasarathy [2] and Meyer [3]. Here I want to discuss some of the more recent developments.
openaire +1 more source