Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has sometimes quite substantial upwards jumps and clusters on high levels. We investigate classical and nonclassical stochastic volatility models with respect to their extreme behavior. We show that classical stochastic volatility models driven by Brownian motion can model heav...

If massive neutrinos possess magnetic moments, they can undergo spin flip in a magnetic field. The magnetic fields needed for a meaningful measurement of neutrino moments could be very high and may occur in astronomical objects such as some supernovae or active galactic nuclei: they are typically chaotic ones. We develop the general theory of the passage of neutrinos through such fields. We als...

We study the connection between Hamiltonian dynamics and irreversible, stochastic equations, such as the Langevin equation. We consider a simple model of a classical harmonic oscillator (Brownian particle) coupled to a field (heat bath). In traditional approaches Langevin-type equations have been derived from Hamiltonian dynamics, but these equations contain memory terms and are both time-rever...

Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has sometimes quite substantial upwards jumps and clusters on high levels. We investigate classical and nonclassical stochastic volatility models with respect to their extreme behavior. We show that classical stochastic volatility models driven by Brownian motion can model heav...

In this work we formulate a consistent Bayesian approach to modeling stochastic (random) dynamical systems by time series and implement it by means of artificial neural networks. The feasibility of this approach for both creating models adequately reproducing the observed stationary regime of system evolution, and predicting changes in qualitative behavior of a weakly nonautonomous stochastic s...