Weak Approximations for Wiener Functionals
N/D
Autores
Leão, Dorival
Ohashi, Alberto Masayoshi Faria
Orientador
Co-orientadores
Citações na Scopus
Tipo de documento
Working Paper
Data
2012
Resumo
In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions and smooth explicit approximations for a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The discretization is given in terms of discrete-jumping filtrations which allow us to approximate non-smooth processes by means of a stochastic derivative operator on the Wiener space. As a by-product, we provide a robust semimartingale approxi mation for weak Dirichlet-type processes.
The underlying semimartingale skeleton is intrinsically constructed in such way that all the relevant structure is amenable to a robust numerical scheme.
In order to illustrate the results, we provide an easily implementable approxi mation scheme for the classical Clark-Ocone formula in full generality. Unlike in previous works, our methodology does not assume an underlying Markovian structure and does not require Malliavin weights. We conclude by proposing a method that enables us to compute optimal stopping times for possibly non Markovian systems arising e.g. from the fractional Brownian motion.
Palavras-chave
Titulo de periódico
URL da fonte
Título de Livro
URL na Scopus
Idioma
Inglês
Notas
Membros da banca
Área do Conhecimento CNPQ
Ciências Exatas e da Terra
Ciências Sociais Aplicadas
Ciências Sociais Aplicadas