@article {IOPORT.05941058,
    author       = {Dumas, W.M. and Tretyakov, M.V.},
    title        = {Computing conditional Wiener integrals of functionals of a general form.},
    year         = {2011},
    journal      = {IMA Journal of Numerical Analysis},
    volume       = {31},
    number       = {3},
    issn         = {0272-4979},
    pages        = {1217-1251},
    publisher    = {Oxford University Press, Oxford},
    doi          = {10.1093/imanum/drq008},
    abstract     = {Let $C_{0,a;T,b}^d$ be the set of all $d$-dimensional continuous vector functions $x(t)$ over $[0,T]$ satisfying $x(0) = a$ and $x(T) = b$. The authors consider the conditional Wiener integral $$ \int_{C_{0,a;T,b}^d}\, F(x(\cdot))\, d\mu_{0,a}^{T,b}(x), $$ where $F$ is a functional on $C_{0,a;T,b}^d$ and $\mu_{0,a}^{T,b}(x)$ is the conditional Wiener measure, corresponding to the $d$-dimensional Brownian bridge from $a$ at the time $t=0$ to $b$ at the time $t=T$. Such path integrals appear in quantum mechanics. In this paper, the authors propose a probabilistic numerical method of second order of accuracy for computing conditional Wiener integrals of sufficiently smooth functionals. The numerical method is based on the simulation of the $d$-dimensional Brownian bridge by a system of stochastic differential equations and on ideas of the weak-sense numerical integration of stochastic differential equations. This yields an efficient and simple algorithm for computing the conditional Wiener integral. A convergence theorem for this method is proved. Special attention is paid to integral-type functionals $F$. A generalization to the case of pinned diffusions is given, too. Finally, numerical experiments are presented.},
    reviewer     = {Manfred Tasche (Rostock)},
    identifier   = {05941058},
}