# Nonlinear L'evy Processes and their Characteristics

arXiv: https://arxiv.org/abs/1401.7253 · HTML: https://mlsanity.com/paper/1401.7253/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2014.

## Built on by (most cited first, 1 of 1)

- [Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits](https://mlsanity.com/paper/2601.01877/) (2026)

## Abstract (arXiv)

We develop a general construction for nonlinear L'evy processes with given characteristics. More precisely, given a set Theta of L'evy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical L'evy processes with triplets in Theta. The nonlinear L'evy process yields a tractable model for Knightian uncertainty about the distribution of jumps for which expectations of Markovian functionals can be calculated by means of a partial integro-differential equation.