Vladimirov-Type Approximation of Wiener Integrals of Suitably Dominated Functionals
نویسندگان
چکیده
منابع مشابه
Approximation of a Class of Wiener Integrals*
and since evaluation of this integral by analysis often cannot be done, it is of some practical interest to investigate the possibility of numerically evaluating this integral. Such a calculation is expected to require an enormous amount of arithmetic since it involves the evaluation of a fc-fold integral where k >5> 1 ; an exact evaluation requires going to the limit k —* ». Consequently, it i...
متن کاملComputing conditional Wiener integrals of functionals of a general form
A numerical method of second order of accuracy for computing conditional Wiener integrals of smooth functionals of a general form is proposed. The method is based on simulation of Brownian bridge via the corresponding stochastic di¤erential equations (SDEs) and on ideas of the weak-sense numerical integration of SDEs. A convergence theorem is proved. Special attention is paid to integral-type f...
متن کاملBrownian excursions, stochastic integrals, and representation of Wiener functionals
A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener f...
متن کاملSeries expansion of Wiener integrals via block pulse functions
In this paper, a suitable numerical method based on block pulse functions is introduced to approximate the Wiener integrals which the exact solution of them is not exist or it may be so hard to find their exact solutions. Furthermore, the error analysis of this method is given. Some numerical examples are provided which show that the approximation method has a good degree of accuracy. The main ...
متن کاملNumerical Evaluation of Wiener Integrals
Here, Jc F[x]w(dx) denotes the Wiener integral, and / F[0(u, ■ )]v(du) denotes an integral over some Euclidean space. In [1] Cameron determined a pair (v, 0) by imposing on (1.2) the condition that the formula be exact for polynomial functionals of degree ^3. Imposing the same requirement, Vladimirov [5] constructed a family of pairs (v, 6). In this paper we shall develop a class of approximati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1968
ISSN: 0002-9947
DOI: 10.2307/1994853