Weak Approximations for Wiener Functionals

dc.contributor.authorLeão, Dorival
dc.contributor.authorOhashi, Alberto Masayoshi Faria
dc.coverage.cidadeSão Paulopt_BR
dc.coverage.paisBrasilpt_BR
dc.creatorLeão, Dorival
dc.creatorOhashi, Alberto Masayoshi Faria
dc.date.accessioned2023-07-24T16:32:21Z
dc.date.available2023-07-24T16:32:21Z
dc.date.issued2012
dc.description.abstractIn 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.
dc.description.otherAbstract. 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 approximation 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 approximation 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 nonMarkovian systems arising e.g. from the fractional Brownian motion.pt_BR
dc.format.extent25 p.pt_BR
dc.format.mediumDigitalpt_BR
dc.identifier.issueBEWP 162/2012
dc.identifier.urihttps://repositorio.insper.edu.br/handle/11224/5915
dc.language.isoInglêspt_BR
dc.publisherInsperpt_BR
dc.relation.ispartofseriesInsper Working Paperpt_BR
dc.rights.licenseO INSPER E ESTE REPOSITÓRIO NÃO DETÊM OS DIREITOS DE USO E REPRODUÇÃO DOS CONTEÚDOS AQUI REGISTRADOS. É RESPONSABILIDADE DO USUÁRIO VERIFICAR OS USOS PERMITIDOS NA FONTE ORIGINAL, RESPEITANDO-SE OS DIREITOS DE AUTOR OU EDITORpt_BR
dc.titleWeak Approximations for Wiener Functionalspt_BR
dc.typeworking paper
dspace.entity.typePublication
local.subject.cnpqCiências Exatas e da Terrapt_BR
local.subject.cnpqCiências Sociais Aplicadaspt_BR
local.typeWorking Paperpt_BR

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