A Stochastic Diffusion Process for the Dirichlet Distribution

A Stochastic Diffusion Process for the Dirichlet Distribution

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a couplednonlinear diffusionprocess is required: theWiener processes in the equivalent systemof stochastic differential equations are multipli...

Lecture 24 : Dirichlet distribution and Dirichlet Process

Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process

The two parameter Poisson-Dirichlet distribution PD(α, θ) is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman’s Poisson-Dirichlet distribution. The two parameter Dirichlet process Πα,θ,ν0 is the law of a pure atomic random measure with masses following the two parameter Poisson-Dirichlet distribution. In this article we focus on the cons...

Consistency Analysis for the Doubly Stochastic Dirichlet Process

This technical report proves components consistency for the Doubly Stochastic Dirichlet Process [1] with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi cluster also support the consistency proof. This report is also a support do...

A Stochastic Diffusion Process of Financial innovation

In this paper, a stochastic diffusion model of a Financial Innovation introducing to a financial institute is presented in order to validate the influence of the diffusion speed in any business line with different rates. The paper is structured in three sections. In section 1 we discuss and analyzing the FI and in section 2 we represent a stochastic process that shows the diffusion of FI, with ...