We develop a hydrodynamic formulation of fractional fluctuations in a viscoelastic liquid whose longitudinal modulus is a scalar and only depends on time. The method is based on the introduction of fractional time derivatives in the hydrodynamic equations due to the viscoelastic memory. Coupled...

The distribution of price returns is studied for a class of market models with Markovian dynamics. The models have a non-constant diffusion coefficient that depends on the value of the return. An analytical expression for the distribution of returns is obtained, and shown to match the results of...

We analyze a specific class of random systems that, while being driven by a symmetric Lévy stable noise, asymptotically set down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) ρ∗(x)∼exp[−Φ(x)]. This behavior needs to be contrasted with the...

We study the long time asymptotics of probability density functions (pdfs) of Lévy flights in confining potentials that originate from inhomogeneities of the environment in which the flights take place. To this end we employ two model patterns of dynamical behavior: Langevin-driven and...

Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process xi with memory as, e.g., a Volterra equation driven by a Levy process. Moreover, the interest rate and a risk premium rho...

The Japanese monetary authority intervenes into the foreign exchange market on and off. The influence of the operations on the fluctuation of the yen exchange rate to U.S. dollar is examined in the period of September 17 through 28, 2001. A cyclic behavior is found in correlation functions of...

A relation giving a minimum for the irreversible work in quasi-equilibrium processes was derived by Sekimoto et al. [K. Sekimoto, S. Sasa, J. Phys. Soc. Japan 66 (1997) 3326] in the framework of stochastic energetics. This relation can also be written as a type of “uncertainty principle” in...

We study the dynamics of ordering of the nonconserved and conserved Heisenberg magnet. The dynamics consists of two parts — an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches both to T=0 and Tc, we show...

In this work we derive a generalized Langevin equation that describes the translational Brownian motion of a tracer particle which interacts with other diffusing particles in the system. The direct interactions of the tracer with these other diffusing particles give rise to memory effects...