The neural network are trained with 600 episodes and the Ornstein-Uhlenbeck process
is declined linearly in [10.sup.4] frames.
Goutte, "Estimation of levy-driven ornstein-uhlenbeck processes
: application to modeling of [Co.sub.2] and fuel-switching," Annals of Operations Research, vol.
Wylomanska, "Subordinated [alpha][alpha]- stable Ornstein-Uhlenbeck process
as a tool for financial data description," Physica A: Statistical Mechanics and its Applications, vol.
References [17, 18] discussed the first three moments of homogeneous portfolios of life insurance and endowment policies by modeling the force of interest directly based on the Wiener process or the Ornstein-Uhlenbeck process
and  also generalized these results to heterogeneous portfolios.
Under the assumption that volatility of the underlying asset obeys a fast mean-reverting Ornstein-Uhlenbeck process
, we study the pricing problem of the collar option by singular perturbation analysis.
. In this subsection we consider the optimal stopping problem when X is an Ornstein-Uhlenbeck process
The study was conducting by starting with reviewing the literature regarding the Brownian motion, Wiener process, Ito process, Ornstein-Uhlenbeck process
and reaching the random walk theory.
The Ornstein-Uhlenbeck process
also fits an autocorrelation.
Note that [L.sub.0] is the infinitesimal generator of the Ornstein-Uhlenbeck process
This paper contributes to the expositions on theoretical and practical aspects of parameter estimation for long-memory stochastic volatility which follows a fractional Ornstein-Uhlenbeck process
. Firstly, we obtain the variance of the stationary version solution to the fractional Ornstein-Uhlenbeck process
, which is important in identifying the variogram function.
At first we simulated an Ornstein-Uhlenbeck process
solution of the stochastic differential equation
This Introduction consists of three first Subsections 1.1, 1.2, 1.3, which are devoted respectively to the presentation of the necessary prerequisites about the Lamperti correspondence, the pseudo-stable increasing processes, and the radial Ornstein-Uhlenbeck processes
. We then state an identity in law (12), between two subordinators, which is the main object of this paper.