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Information upper bound for McKean-Vlasov stochastic differential equations
Li Lv1, Yanjie Zhang2, Zibo Wang1
1School of Mathematics and Statistics and Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.
Chaos (Woodbury, N.Y.)
|July 9, 2021
Summary
We developed an information-theoretic framework to establish an upper bound for probability distributions in McKean-Vlasov stochastic differential equations, using Kullback-Leibler divergence.
Area of Science:
- Stochastic Analysis
- Information Theory
- Probability Theory
Background:
- McKean-Vlasov stochastic differential equations model systems with interacting particles.
- Quantifying information in these complex systems is crucial for understanding their behavior.
- Existing methods may not fully capture the information dynamics.
Purpose of the Study:
- To develop a novel information-theoretic framework.
- To quantify the information upper bound for probability distributions of McKean-Vlasov SDE solutions.
- To analyze the relationship between system entropy and mean-field approximations.
Main Methods:
- Information-theoretic framework development.
- Derivation of Kullback-Leibler divergence for entropy characterization.
- Analysis of probability distributions for McKean-Vlasov SDEs.
- Investigation of mean-field particle systems.
Main Results:
- Established an information upper bound for McKean-Vlasov SDE solutions.
- Quantified this bound using Kullback-Leibler divergence.
- Characterized the entropy of solution distributions relative to mean-field systems.
- Determined the order of the information upper bound.
Conclusions:
- The developed framework provides a rigorous method for bounding information in McKean-Vlasov SDEs.
- Kullback-Leibler divergence is a key metric for this quantification.
- The findings offer insights into the information flow and complexity of mean-field systems.
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