Nonlinear L\'evy and nonlinear Feller processes: an analytic introduction

TL;DR

This paper provides an accessible, abstract introduction to the analytical foundations of nonlinear Le9vy and Feller processes, a rapidly developing area in nonlinear Markov process theory.

Contribution

It offers a concise, more abstract overview of the analytical aspects of nonlinear Le9vy and Feller processes, expanding on prior foundational work.

Findings

Introduces the basic analytical framework for nonlinear Le9vy processes.

Summarizes key developments in nonlinear Markov processes.

Highlights the importance of the topic for future research.

Abstract

The program of studying general nonlinear Markov processes was put forward in V. N. Kolokoltsov "Nonlinear Markov Semigroups and Interacting L\'evy Type Processes" (Journ. Stat. Physics 126:3 (2007), 585-642), and was developed by the author in monograph "Nonlinear Markov processes and kinetic equations". Cambridge University Press, 2010, where, in particular, nonlinear L\'evy processes were introduced. The present paper is an invitation to the rapidly developing topic of noninear Markov processes. We provide a quick (and at the same time more abstract) introduction to the basic analytical aspects of the theory developed in Part II of the above mentioned book.