Maximum entropy principle handled by using complex fractional moments

Abstract

A novel Maximum Entropy Principle method constrained by Complex Fractional Moments is proposed in this paper, which can be applied for reconstructing of approximate probability distribution equations with few complex fractional moments. By introducing complex fractional moments with different imaginary parameters into the entropy functional, an extended entropy functional with unknown Lagrange multipliers is constructed, which is utilized for deriving the approximate probability density function. The new method is extended to obtaining probability density function in stochastic dynamic systems based on the complex fractional moment equations which is derived from Fokker–Planck-Kolmogorov equation. Numerical simulations verified the effectiveness of the approach.