Abstract
In this work we introduce a Brownian motion in random environment which is a Brownian constructions by an exchangeable sequence based on Dirichlet processes samples. We next compute a stochastic calculus and an estimation of the parameters is computed in order to classify a functional data.
Highlights
The Brownian motion is a very interesting tool for both theoretical and applied math
Despite its recent introduction to the literature, hierarchical models with a Dirichlet prior, shortly Dirichlet hierarchical models, were used in probabilistic classification applied to various fields such as biology [1], astronomy [2] or text mining [3] and finance [4]-[6]
The aim of this paper is to extend these models and estimate their parameters in order to deal with temporal data following a stochastic differential equation (SDE)
Summary
The Brownian motion is a very interesting tool for both theoretical and applied math. Despite its recent introduction to the literature, hierarchical models with a Dirichlet prior, shortly Dirichlet hierarchical models, were used in probabilistic classification applied to various fields such as biology [1], astronomy [2] or text mining [3] and finance [4]-[6]. These models can be seen as complex mixtures of real Gaussian distributions fitted to non-temporal data.
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