Work

Donsker-Type Construction for the Self-Stabilizing and Self-Scaling Process

Year: 2025

Type: article

Abstract: Using a Donsker-type construction, we prove the existence of a new class of processes, which we call the self-stabilizing processes. These processes have a particular property: the “local intensities of jumps” vary with the values. Moreover, we also show that the self-stabilizing processes have many other good properties, such as stochastic Hölder continuity and strong localizability. Such a self-stabilizing process is simultaneously a Markov process, a martingale (when the local index of stability is greater than 1), a self-scaling process and a self-regulating process.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9100677

Authors: Xiequan Fan, Jacques Lévy Véhel

Institution: Northeastern University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Natural Science Foundation of Hebei Province