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The Inequality Process as a wealth maximizing process

机译：不平等过程是财富最大化的过程

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The One Parameter Inequality Process (OPIP) long predates the Saved Wealth Model (SWM) to which it is isomorphic up to the different choice of stochastic driver of wealth exchange. Both are stochastic interacting particle systems intended to model wealth and income distribution. The OPIP and other versions of the Inequality Process explain many aspects of wealth and income distribution but have gone undiscussed in econophysics. The OPIP is a jump process with a discrete 0, 1 uniform random variate driving the exchange of wealth between two particles, while the SWM, as an extension of the stochastic version of the ideal gas model, is driven by a continuous uniform random variate with support at [0.0, 1.0]. The OPIP's stationary distribution is a Levy stable distribution attracted to the Pareto pdf near the (hot) upper bound of the OPIP's parameter, omega, and attracted to the normal (Gaussian) pdf toward the (cool) lower bound of omega. A gamma pdf model approximating the OPIP's stationary distribution is heuristically derived from the solution of the OPIP. The approximation works for omega < .5, better as omega -> 0. The gamma pdf model has parameters in terms of w. The Inequality Process with Distributed Omega (IPDO) is a generalization of the OPIP. In the IPDO each particle can have a unique value of its parameter, i.e., particle i has omega(i). The meta-model of the Inequality Process implies that smaller omega is associated with higher skill level among workers. This hypothesis is confirmed in a test of the IPDO. Particle wealth gain or loss in the OPIP and IPDO is more clearly asymmetric than in the SWM (lambda not equal 0 0). Time-reversal asymmetry follows from asymmetry of gain and loss. While the IPDO scatters wealth, it also transfers wealth from particles with larger omega to those with smaller omega, particles that according to the IPDO's meta-model are more productive of wealth, nourishing wealth production. The smaller the harmonic mean of the omega(i)'s in the IPDO population of particles, the more wealth is concentrated in particles with smaller omega, the less noise and the more omega signal there is in particle wealth, and the deeper the time horizon of the process. The IPDO wealth concentration mechanism is simpler than Maxwell's Demon. Published by Elsevier B.V.
机译：单参数不平等过程（OPIP）早于保存财富模型（SWM）之前，同构模型一直到财富交换的随机驱动因素的不同选择。两者都是旨在模拟财富和收入分配的随机相互作用粒子系统。 OPIP和其他版本的《不平等过程》解释了财富和收入分配的许多方面，但在经济学中没有得到讨论。 OPIP是一个跳跃过程，具有离散的0、1均匀随机变量，驱动两个粒子之间的财富交换，而SWM，作为理想气体模型的随机版本的扩展，由连续均匀的随机变量驱动。支撑为[0.0，1.0]。 OPIP的平稳分布是一个Levy稳定分布，在OPIP参数Ω的（热）上限附近被吸引到Pareto pdf，并在Ω的（冷）下限吸引到正态（高斯）pdf。启发式地从OPIP的解决方案中得出一个近似于OPIP固定分布的γpdf模型。近似适用于omega <.5，最好是omega->0。gamma pdf模型具有以w表示的参数。分布式欧米茄不平等过程（IPDO）是OPIP的概括。在IPDO中，每个粒子可以具有其参数的唯一值，即粒子i具有omega（i）。不平等过程的元模型表明，欧米茄越小，工人的技能水平越高。在IPDO的测试中证实了这一假设。与SWM中相比，OPIP和IPDO中的粒子财富获得或损失更加不对称（λ不等于0 0）。时间反转不对称源自增益和损耗的不对称。 IPDO在分散财富的同时，也将财富从欧米茄较大的颗粒转移到欧米茄较小的颗粒，根据IPDO元模型，那些颗粒会更富裕地生产财富，从而促进财富生产。 IPDO粒子总体中欧米伽（i）的谐波平均值越小，则更多的财富集中在欧米伽较小的粒子中，噪声越小，并且粒子财富中的欧米伽信号越多，时间越深过程的视界。 IPDO财富集中机制比Maxwell的Demon简单。由Elsevier B.V.发布

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