Analysis and application of multiplicative stochastic process with a sample-dependent lower bound

TL;DR

This paper investigates a multiplicative stochastic process with a lognormally distributed lower bound, deriving its distribution and properties, and validating the model against real data to demonstrate its applicability.

Contribution

It introduces a new model of multiplicative stochastic processes with a sample-dependent lower bound and derives its distribution and statistical properties.

Findings

Theoretical distribution matches empirical data.

Model parameters can be adjusted to fit real data.

Provides a framework for analyzing processes with lower bounds.

Abstract

A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties are derived. By adjusting the parameters, it is confirmed that the theoretical distribution is consistent with empirical distributions of some real data.