Fractional equations via convergence of forms

TL;DR

This paper explores how the convergence of time-changed stochastic processes driven by fractional equations can be understood through the convergence of their associated Dirichlet forms, using a general fractional operator in time.

Contribution

It establishes a link between the convergence of fractional equations and Dirichlet forms, extending the understanding of fractional operators in time.

Findings

Convergence of time-changed processes is characterized by Dirichlet form convergence.

General fractional operators in time are effectively incorporated into the analysis.

The approach provides a new perspective on fractional equations and their stochastic representations.

Abstract

We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in time.