Algebraic theory of causal double products

Year, pages: 2010, 723 - 738

Corresponding to each ``rectangular'' double product in the form of a formal power series $R[h]$ with coefficients in the tensor product $\mathcal{T(L)}\otimes \mathcal{T(L)}$ with itself of the Itô Hopf algebra, we construct ``triangular'' elements $T[h]$ of $\mathcal{T(L)}$ satisfying $\Delta T[h]=T[h]^{(1)}R[h]T\{h]^{(2)}$. In Fock space representations of $\mathcal{T(L)}$ by iterated quantum stochastic integrals when $\mathcal{L}$ is the algebra of Itô differentials of the calculus, these correspond to ``causal'' double product integrals in a single Fock space.

Hudson, R. 2010. Algebraic theory of causal double products. In Mathematica Slovaca, vol. 60, no.5, pp. 723-738. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0042-6

Hudson, R. (2010). Algebraic theory of causal double products. Mathematica Slovaca, 60(5), 723-738. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0042-6