## 83 Citations

### Quantum Lévy–Itô algebras and non-commutative stochastic analysis

- Mathematics
- 2012

We review the basic concepts of quantum probability and revise the classical and quantum stochastic (QS) calculus using the universal Itô B*-algebra approach. A non-commutative generalization of Lévy…

### Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes

- Mathematics
- 2001

A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space and it is shown that they…

### Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale

- Physics, MathematicsArXiv
- 2011

The Fock-Guichardet formalism for the quantum stochastic integration is introduced, and the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS integration over a space-time.

### Noncommutative dynamics is the unified dynamics of quantum and classical systems on a C *-algebra represented in a Hilbert space Γ with a generating state vector

- Mathematics
- 2010

We review the basic concepts of quantum stochastics using the universal Itô *-algebra approach. The main notions and results of classical and quantum stochastics are reformulated in this unifying…

### Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space

- Mathematics
- 2011

We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels in Fock scale. The…

### Noncommutative dynamics and generalized master equations

- Mathematics
- 2010

We review the basic concepts of quantum probability and stochastics using the universal Itô B*-algebra approach. The main notions and results of classical and quantum stochastics are reformulated in…

### Quantum stochastic calculus with maximal operator domains.

- Mathematics
- 2004

Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic…

### Quantum Stochastic Calculus with Maximal Operator Domains 1

- Mathematics
- 2004

Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic…

### A canonical dilation of the Schrödinger equation

- Mathematics, PhysicsRussian Journal of Mathematical Physics
- 2014

In this paper we shall re-visit the well-known Schrödinger equation of quantum mechanics. However, this shall be realized as a marginal dynamics of a more general, underlying stochastic counting…

### A canonical dilation of the Schrödinger equation

- Mathematics, Physics
- 2014

In this paper we shall re-visit the well-known Schrödinger equation of quantum mechanics. However, this shall be realized as a marginal dynamics of a more general, underlying stochastic counting…

## References

SHOWING 1-10 OF 30 REFERENCES

### A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space

- Mathematics
- 1988

An algebraic definition of the basic quantum process for the noncommutative stochastic calculus is given in terms of the Fock representation of a Lie ⋆-algebra of matrices in a pseudo-Euclidean…

### Quantum Ito's formula and stochastic evolutions

- Mathematics
- 1984

Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator…

### Cohomology of power sets with applications in quantum probability

- Mathematics
- 1989

Square integrable Wiener functionals may be represented as sums of multiple Itô integrals. This leads to an identification of such functionals with square integrable functions on the symmetric…

### Reconstruction theorem for a quantum stochastic process

- Mathematics, Physics
- 1985

This paper gives a physically interpretable--in real time--definition of a QSP as families of representations of the observable algebra 'B' in a common (large) system by indicating a universal method…

### Generalized stochastic integrals and the malliavin calculus

- Mathematics
- 1986

SummaryThe paper first reviews the Skorohod generalized stochastic integral with respect to the Wiener process over some general parameter space T and it's relation to the Malliavin calculus as the…

### Quantum Markov processes on Fock space described by integral kernels

- Mathematics
- 1985

A description is introduced of operators on Fock space by way of integral kernels. In terms of these kernels, the quantum stochastic differential equation for a Markov process over the n×n matrices…