We demonstrate that continuous-time FARIMA processes with α-stable noise provide a new stochastic tool for studying the solar flare phenomenon in the framework of fractional Langevin equation. Simple computer tests to check the origins of α-stability and self-similarity are implemented for...

We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency...

In this paper we consider the forward/futures contracts and Asian-type call options for power delivery as important components of the bidding strategies of the players’ profits on the electricity market. We show how these derivatives can affect their profit. We use linear asymmetric supply...

The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to 2nd order stochastic differential equations, subject to large random external disturbances with infinite variance, described by α-stable Lévy motion...

We show that intrinsically random dynamical systems with the Prigogine operator Λ of the form of a random Laplace transform, can be characterized as Kolmogorov flows (K-flows). We also obtain a spectral characterization in the language of the Weyl commutation relation. As a consequence we...

In this paper we consider the forward/futures contracts and Asian-type call options for power delivery as important components of the bidding strategies of the players’ profits on the electricity market. We show how these derivatives can affect their profit. We use linear asymmetric supply...

We derive spectral necessary and sufficient conditions for stationary symmetric stable processes to be metrically transitive and mixing. We then consider some important classes of stationary stable processes: Sub-Gaussian stationary processes and stationary stable processes with a harmonic...

A complex second-order stochastic process {X(t); t [set membership, variant] } is periodically correlated (PC) when its mean function m(t) and covariance R(s, t) are periodic with the period T. In the following note the relationship between the hierarchy of chaos and estimation for the...