Concentration analysis of multivariate elliptic diffusions
Authors: Lukas Trottner, Cathrine Aeckerle-Willems, Claudia Strauch
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove concentration inequalities and associated PAC bounds for both continuous- and discrete-time additive functionals for possibly unbounded functions of multivariate, nonreversible diffusion processes. Our analysis relies on an approach via the Poisson equation allowing us to consider a very broad class of subexponentially ergodic, multivariate diffusion processes. These results add to existing concentration inequalities for additive functionals of diffusion processes which have so far been only available for either bounded functions or for unbounded functions of processes from a significantly smaller class. We demonstrate the power of these exponential inequalities by two examples of very different areas. |
| Researcher Affiliation | Academia | Lukas Trottner EMAIL Department of Mathematics Aarhus University Aarhus, Denmark. Cathrine Aeckerle-Willems EMAIL Department of Economics University of Mannheim Mannheim, Germany. Claudia Strauch EMAIL Department of Mathematics Aarhus University Aarhus, Denmark. |
| Pseudocode | No | The paper describes mathematical proofs and derivations, and analyzes algorithms theoretically, but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statement about open-sourcing the code for the methodology described, nor does it provide a link to a code repository. |
| Open Datasets | No | The paper is theoretical, focusing on mathematical analysis of diffusion processes and algorithms. It does not use or make available any specific experimental datasets. |
| Dataset Splits | No | The paper is theoretical and does not involve experimental datasets or their splits. |
| Hardware Specification | No | The paper is theoretical and describes mathematical proofs and analyses. It does not report on any experiments that would require specific hardware specifications. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical derivations. It does not mention any specific software or library versions used for implementation. |
| Experiment Setup | No | The paper is theoretical and presents mathematical results and analyses. It does not describe any experimental setups, hyperparameters, or training configurations. |