Weakly self-interacting velocity jump processes for bacterial chemotaxis and adaptive algorithms

TL;DR

This paper introduces a self-interacting velocity jump process that mimics self-interacting diffusion, with its normalized occupation measure converging to a deterministic flow, offering new insights into bacterial chemotaxis modeling and adaptive algorithms.

Contribution

The paper presents a novel self-interacting velocity jump process that approximates self-interacting diffusion, providing a new framework for modeling bacterial chemotaxis and adaptive systems.

Findings

Normalized occupation measure converges to a deterministic flow.

Process behavior aligns with self-interacting diffusion in large time.

Offers a new approach for modeling chemotaxis and adaptive algorithms.

Abstract

A self-interacting velocity jump process is introduced, which behaves in large time similarly to the corresponding self-interacting diffusion, namely the evolution of its normalized occupation measure approaches a deterministic flow.