arXiv subjects
Publications and source records attributed to Ryszard Zygadło.
The evolution of prices on ideal market is given by geometrical Brownian motion, where Gaussian white noise describes fluctuations. We study the effect of correlations introduced by a color noise.
It is shown analytically that the flashing annihilation term of a Verhulst kinetic leads to the power--law distribution in the stationary state. For the frequency of switching slower than twice the free growth rate this provides the quasideterministic source of a Levy noises at the macroscopic level.
It is shown that the usual identification of certain averages with the relativistic thermodynamical functions is not possible in the moving reference frame description. The Brownian motion approach is used as the Markovian kinetic description of the relativistic ideal gas system.
The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal corrections, to the both relaxation times $T$ (of stationary autocorrelations) and transient relaxation time of momentum, appear slowing down the processes. The transient relaxation time of the velocity does not depend {\it explicitly} on temperature, $T(v_0)= m(v_0)/γ\equiv ε_0/γc^2$, and it is proportional to the initial energy of a relativistic Brownian particle.
It is shown that the Lorentz invariant temperature $T^\prime=T$ and entropy $S^\prime=γS$, pressure ${\cal P}^\prime = γ^2 {\cal P}$, volume ${\cal V}^\prime ={\cal V}/γ$, and energy $U^\prime = γU$, where $γ= (1-V^2/c^2)^{-1/2}$, are the correct transformational properties of the thermodynamical quantities of the relativistic ideal gas.