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arXiv · 2407.13206

Double stochastic opinion dynamics with fractional inflow of new opinions

Vygintas Gontis
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Abstract

A recent analysis of empirical limit order flow data highlights the necessity for a more refined order flow model that integrates the power-law distribution of limit order cancellation times. These cancellation times follow a discrete probability mass function derived from the Tsallis $q$-exponential distribution, or equivalently, the second form of the Pareto distribution. By combining fractional L'{e}vy stable motion as the model for limit order inflow with the power-law distribution for cancellation times, we propose an innovative approach to modeling order imbalance in financial markets. We extend this model to a broader context, illustrating its applicability to opinion dynamics in social systems where opinions have a finite lifespan. This proposed model exemplifies a stochastic time series characterized by stationary increments and broken self-similarity. Consequently, it offers a novel framework for testing methods to evaluate long-range dependence in such time series.

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Vygintas Gontis. 2024-07-18. Double stochastic opinion dynamics with fractional inflow of new opinions. https://arxiv.org/abs/2407.13206

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