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A backward particle interpretation of Feynman-Kac formulae

Pierre Del Moral, Arnaud Doucet, Sumeetpal S. Singh (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals “on-the-fly” as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We...

A note on impulsive control of Feller processes with costly information

Dariusz Gątarek (1990)

Aplikace matematiky

The paper deals with the optimal inspections and maintenance problem with costly information for a Markov process with positive discount factor. The associated dynamic programming equation is a quasi-variational inequality with first order differential terms. In this paper we study its different formulations: strong, visousity and evolutionary. The case of impulsive control of purely jump Markov processes is studied as a special case.

A recursive robust Bayesian estimation in partially observed financial market

Jianhui Huang (2007)

Applicationes Mathematicae

I propose a nonlinear Bayesian methodology to estimate the latent states which are partially observed in financial market. The distinguishable character of my methodology is that the recursive Bayesian estimation can be represented by some deterministic partial differential equation (PDE) (or evolution equation in the general case) parameterized by the underlying observation path. Unlike the traditional stochastic filtering equation, this dynamical representation is continuously dependent on the...

An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

Application of the random field theory in PET imaging - injection dose optimization

Jiří Dvořák, Jiří Boldyš, Magdaléna Skopalová, Otakar Bělohlávek (2013)

Kybernetika

This work presents new application of the random field theory in medical imaging. Results from both integral geometry and random field theory can be used to detect locations with significantly increased radiotracer uptake in images from positron emission tomography (PET). The assumptions needed to use these results are verified on a set of real and simulated phantom images. The proposed method of detecting activation (locations with increased radiotracer concentration) is used to quantify the quality...

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