Stochastic processes via the pathway model

TL;DR

This paper introduces a flexible pathway model for stochastic processes that allows switching between different probability distributions, enabling better modeling of physical systems with various tail behaviors.

Contribution

It presents a novel pathway approach to generate diverse stochastic models with adjustable tail properties, enhancing modeling capabilities for physical phenomena.

Findings

Provides techniques to produce thicker or thinner tails in models

Introduces the pathway parameter for switching distribution forms

Applicable to reaction, diffusion, and reaction-diffusion systems

Abstract

After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the input-output type mechanism is considered first, where reaction, diffusion, reaction-diffusion, and production-destruction type physical situations can fit in. Then techniques are described to produce thicker or thinner tails (power law behavior) in stochastic models. Then the pathway idea is described where one can switch to different functional forms of the probability density function) through a parameter called the pathway parameter.