105 citations · 529 across the 26 of their papers we have counts for
8 papers · 1 filter
Fokker-Planck and Chapman-Kolmogorov equations for Ito processes with finite memory
Joseph L. McCauley
The usual derivation of the Fokker-Planck partial differential eqn. assumes the Chapman-Kolmogorov equation for a Markov process. Starting instead with an Ito stochastic differenti…
Markov vs. nonMarkovian processes A comment on the paper Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations by T.D. Frank
Joseph L. McCauley
The purpose of this comment is to correct mistaken assumptions and claims made in the paper Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck…
Hurst Exponents, Markov Processes, and Fractional Brownian motion
Joseph L. McCauley, Gemunu H. Gunaratne, Kevin E. Bassler
There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illu…
Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance
Kevin E. Bassler, Gemunu H. Gunaratne, Joseph L. McCauley
We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motio…
A theory for Fluctuations in Stock Prices and Valuation of their Options
Gemunu H. Gunaratne, Joseph L. McCauley
A new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stoc…
Nonintegrability, Chaos, and Complexity
J. L. McCauley
Two-dimensional driven dissipative flows are generally integrable via a conservation law that is singular at equilibria. Nonintegrable dynamical systems are confined to n*3 dimensi…
The Hentschel-Procaccia Conjecture
J. L. McCauley
Extensive confusion exists and persists in the literature on dynamical systems theory, cosmology, and other fields over spectra of fractal dimensions. Entirely different generating…
The Futility of Utility: how market dynamics marginalize Adam Smith
Joseph L. McCauley
Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists…