Critical link of self-similarity and visualisation for jump-diffusions driven by $\alpha$-stable noise

TL;DR

This paper establishes a key relationship between parameters governing self-similar jump-diffusions driven by alpha-stable noise, using multivariate interpolation and visualization to deepen understanding of their trajectories.

Contribution

It introduces a novel parameter linkage for self-similar jump-diffusions driven by alpha-stable noise, combining theoretical interpolation with computational visualization.

Findings

Identified critical parameter relationships for self-similar jump-diffusions.

Visualized trajectories for various parameter combinations.

Enhanced understanding of jump-diffusion behaviors through simulation.

Abstract

The purpose of this paper is to derive a critical link of parameters for the self-similar trajectories of jump-diffusions which are described as solutions of stochastic differential equations driven by $\alpha$-stable noise. This is done by a multivariate Lagrange interpolation approach. To this end, we utilise computer simulation algorithm in MATLAB to visualise the trajectories of the jump-diffusions for various combinations of parameters arising in the stochastic differential equations.