Malliavin calculus with time dependent coefficients and application to nonlinear filtering
type: Item
instance of: scholarly article
title: Malliavin calculus with time dependent coefficients and application to nonlinear filtering
zbMATH Open document ID: 0677.60059
DOI: 10.1007/BF01474642
author: Patrick Florchinger
publication date: 1990-01-01T00:00:00Z
review text: We prove, using Malliavin calculus, that under a local Hörmander condition the solution of a stochastic differential equation with time- depending coefficients admits a \(C^{\infty}\) density with respect to Lebesgue measure. An application of this result to nonlinear filtering is developed to prove the existence of a \(C^{\infty}\) density for the filter associated with a correlated system whose observation is one dimensional with unbounded coefficients.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 4109766
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: Hoermander condition
zbMATH Keywords: nonlinear filtering
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4109766