We incorporate randomness into deterministic theories and compare analytically and numerically some well-known stochastic theories: the Liouville process, the Ornstein-Uhlenbeck process, and a process that is Gaussian and exponentially time correlated Ornstein-Uhlenbeck noise . Different methods of achieving the marginal densities for correlated and uncorrelated noise are discussed. Analytical ...

The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on Lévy driven Ornstein-Uhlenbeck (OU) type processes. Discrete superpositions of these processes can be constructed to incorporate non-Gaussian marginal distributions and long or short range dependence. While the partial sums of finite superpositions of OU type pr...

The recent deregulation of electricity markets has led to the creation of energy exchanges, where the electricity is freely traded. In this paper, we study the most salient statistical features of electricity prices with a particular attention to the European energy exchanges. These features can be adequately reproduced by the sum-OU model: a model representing the price as a sum of Lévy-driven...

An α-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter α > 0 represents a mean reversion force to zero. We generalize the notion of α-Wiener bridges to continuous functions α : [0, T ) → R. We show that if the limit limt↑T α(t) exists and is positive, then a general α-Wiener bridge is in fact a bridge in the sense that it converges to 0 at time T wi...

‎in this paper lie symmetry analysis is applied in order to find new solutions for fokker plank equation of ornstein-uhlenbeck process‎. ‎this analysis classifies the solutions format of the fokker plank equation by using the lie algebra of the symmetries of our considered stochastic process‎.

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of well-known univariate OU process to bivariate time series. This maps out stochastic oscillations over in complex plane, are observed many applications coupled The appeal model that generated using one simple first order SDE, whereas alternative models require more complicated vectorised or higher SDE repre...