Using Stein’s method and the Malliavin calculus of variations, we derive explicit estimates for the Gamma approximation of functionals of a Poisson measure. In particular, conditions are presented under which the distribution of a sequence of multiple Wiener-Itô stochastic integrals with respect to a compensated Poisson measure converges to a Gamma distribution. As an illustration, we present a...

After a review of how Boson Fock space (of arbitrary multiplicity) may be approximated by a countable Hilbert-space tensor product (known as toy Fock space) it is shown that vacuum-adapted multiple quantum Wiener integrals of bounded operators may be expressed as limits of sums of operators defined on this toy space, with strong convergence on the exponential domain. The vacuum-adapted quantum ...

We consider the class of all the Hermite processes (Z t )t2[0;1] of order q 2 N and with Hurst index H 2 ( 1 2 ; 1). The process Z (q;H) is H-self-similar, it has stationary increments and it exhibits long-range dependence identical to that of fractional Brownian motion (fBm). For q = 1, Z is fBm, which is Gaussian; for q = 2, Z is the Rosenblatt process, which lives in the second Wiener chaos;...

In many modelling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary diierential equation (SODE). However, unlike the de-terministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by Burrage and Bu...

The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in form of a composition characteristics used mathematical description control systems. This can be defined relative various orthonormal bases. For given deterministic square-integrable kernels, characteristic operator determined as an infinite random matrix. main applications such su...