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 [9].
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.
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 [6] for this constant to hold.