Parameter estimation for stochastic diffusion process

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 $\sigma$.