Malliavin calculus for difference approximations of multidimensional diffusions: Truncated local limit theorem
نویسندگان
چکیده
منابع مشابه
Central Limit Theorem for a Stratonovich Integral with Malliavin Calculus
The purpose of this paper is to establish the convergence in law of the sequence of “midpoint” Riemann sums for a stochastic process of the form f ′(W ), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-ofvariable formula in law with a second order correction term which is an Itô integral of f ′′(W ) with respect to...
متن کاملNormal approximations with Malliavin calculus
This monograph contains some recent results by the authors and their collaborators on the application of Stein’s method combined with Malliavin calculus to the normal approximation for functionals of a Gaussian process. It is addressed to researchers and graduate students in probability and statistics who would like to learn the basis of Gaussian analysis and its application to asymptotic techn...
متن کاملDifference Approximation for Local times of Multidimensional Diffusions
Abstract. We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W -functional of the limiting process. The class of the W -functionals, that can be obtained as the limiting ones, is completely described in the terms of the associated W -...
متن کاملLectures on Gaussian approximations with Malliavin calculus
Overview. In a seminal paper of 2005, Nualart and Peccati [40] discovered a surprising central limit theorem (called the “Fourth Moment Theorem” in the sequel) for sequences of multiple stochastic integrals of a fixed order: in this context, convergence in distribution to the standard normal law is equivalent to convergence of just the fourth moment. Shortly afterwards, Peccati and Tudor [46] g...
متن کاملWeak approximations. A Malliavin calculus approach
We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that may be anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore, if the inve...
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: Ukrainian Mathematical Journal
سال: 2008
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-008-0065-0