Furthermore, the findings of ergodicity
and stationarity also demonstrate that the series do not meet the assumptions of conventional diffusion models of log-normal price prevailing in the theoretical finance literature.
Chaotic systems have properties like ergodicity
, sensitivity to initial condition, mixing property, and also have deterministic dynamic and complex structure.
They cover mechanics, molecular dynamics, and Gibbs' statistical mechanics; numerical integration and error analysis; molecular dynamics with thermostats; simple systems with thermal constraints; ergodicity
and its importance in small systems; equilibrium thermodynamics + non-equilibrium hydrodynamics; the statistical mechanics of small systems; microscopic reversibility, macroscopic irreversibility; Lyapunov instability, fractals, and chaos; and smooth particle continuum mechanics.
Further, with an ergodicity
hypothesis, the image distribution is estimated from its pixels.
Zhu, "Stationary distribution and ergodicity
of a stochastic hybrid competition model with Levy jumps," Nonlinear Analysis: Hybrid Systems, vol.
For cryptography, chaotic systems can be broadly implemented to encrypt biometric characteristics due to their intrinsic properties, such as ergodicity
, mixture, and sensitivity to their parameters and initial conditions .
Due to ergodicity
hypothesis volume averaging is equal to statistical averaging: [mathematical expression not reproducible].
Markin, "On the mean ergodicity
of weak solutions of an abstract evolution equation," Methods of Functional Analysis and Topology, vol.
Performance analysis is provided to show that 2D-SLMM has wider chaotic range, better ergodicity
, and hyperchaotic properties than the existing chaotic maps.
Liu, "Stationary distribution and ergodicity
of a stochastic food-chain model with Levy jumps," Physica A: Statistical Mechanics and its Applications, vol.
Chaos, as a widespread nonlinear phenomenon in nature, has the characteristics of randomness, ergodicity
, sensitivity to initial conditions and so on .
We analyze the largest possible [C.sup.V.sub.[infinity]]([[chi].sub.[omega]]), over all [omega] [member of] [M.sub.L], and we develop conditions analogous to the quantum unique ergodicity
conditions in  for this constant to hold.