# Stochastic modelling of non-stationary financial assets

## TL;DR

This paper introduces a stochastic modeling framework for non-stationary financial volume-price data using Langevin equations, capturing the dynamics of distribution parameters and reconstructing empirical statistics effectively.

## Contribution

It presents a novel approach to model non-stationary financial data by deriving Langevin equations for distribution parameters directly from empirical time series.

## Key findings

- Parameters' time series are stationary and Markov-like.
- Reconstructed volume-price distribution moments match empirical data.
- Framework applicable to other non-stationary stochastic variables.

## Abstract

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely biology, medicine and geology.