Piecewise Constant Approximation for the Monte-Carlo Calculation of Wiener Integrals

Computing conditional Wiener integrals of functionals of a general form

“…This method is analogous to the one used in the case of the usual (unconditional) Wiener measure [27] (see also [20]). We prove the following convergence theorem.…”

“…In [10,27] (see also [20]), the probabilistic approach was used for computing Wiener integrals with respect to the usual (unconditional) Wiener measure. In [19] (see also [20]) this approach was exploited to compute conditional Wiener integrals of exponential-type functionals.…”

“…In [19] (see also [20]) this approach was exploited to compute conditional Wiener integrals of exponential-type functionals. Here, on the one hand, we deal with a more complicated system than in [10,27], since the SDEs involved in the method are singular. This leads to a rather sophisticated proof of the method's convergence, requiring some new ideas.…”

“…On the other hand, we consider a much wider class of functionals than in [19]. The proposed method is new in comparison with the ones available in [19] and it is analogous to the one used in the case of the usual Wiener measure [27]. We also note that there are a large number of methods and results (see, e.g.…”

“…But not much attention (except, e.g. [17,20,27]) has been paid to approximating general functionals depending on trajectories of the SDE solution. Other approaches to computing Wiener integrals can be found, e.g.…”