Parameter estimation for stochastic diffusion process

TL;DR

This paper introduces a new stochastic diffusion process with a Weibull-based drift, providing explicit solutions and parameter estimation methods using maximum likelihood from discrete samples.

Contribution

It proposes a novel diffusion process with Weibull-based drift and develops maximum likelihood estimation techniques for its parameters.

Findings

Explicit probabilistic solution of the new process.

Effective maximum likelihood estimation from discrete data.

Parameters estimated successfully using the proposed method.

Abstract

In the present paper we propose a new stochastic diffusion process with drift proportional to the Weibull density function defined as X $\epsilon$ = x, dX t = $\gamma$ t (1 - t $\gamma$+1) - t $\gamma$ X t dt + $\sigma$X t dB t , t \textgreater{} 0, with parameters $\gamma$ \textgreater{} 0 and $\sigma$ \textgreater{} 0, where B is a standard Brownian motion and t = $\epsilon$ is a time proche to zero. First we interested to probabilistic solution of this process as the explicit expression of this process. By using the maximum likelihood method and by considering a discrete sampling of the sample of the new process we estimate the parameters $\gamma$ and $\sigma$.