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Mean field analysis of interacting network model with jumps

Zeqian Li

TL;DR

The strong well-posedness of the associated McKean–Vlasov equation and a corresponding propagation of chaos result are proven and precise estimates of the convergence speed with respect to a Wasserstein-like metric are provided.

Abstract

This paper considers an $n$-particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as $n\to\infty$ of the empirical measure of the jump-diffusions to the solution of a deterministic McKean-Vlasov equation. The strong well-posedness of the associated McKean-Vlasov equation and a corresponding propagation of chaos result are proven. In particular, we provide also precise estimates of the convergence speed with respect to a Wasserstein-like metric.

Mean field analysis of interacting network model with jumps

TL;DR

The strong well-posedness of the associated McKean–Vlasov equation and a corresponding propagation of chaos result are proven and precise estimates of the convergence speed with respect to a Wasserstein-like metric are provided.

Abstract

This paper considers an -particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as of the empirical measure of the jump-diffusions to the solution of a deterministic McKean-Vlasov equation. The strong well-posedness of the associated McKean-Vlasov equation and a corresponding propagation of chaos result are proven. In particular, we provide also precise estimates of the convergence speed with respect to a Wasserstein-like metric.
Paper Structure (8 sections, 2 theorems, 63 equations)

This paper contains 8 sections, 2 theorems, 63 equations.

Table of Contents

  1. Introduction
  2. Model
  3. Jump diffusion model
  4. Mean field model
  5. Mean field analysis
  6. Propagation of chaos
  7. Propagator of FPK equation
  8. Metric and convergence of to

Key Result

Theorem 4

Let the assumptions (A$_{ini}$), (A$_{\overline{f}\overline{g}h}$), (A$_{\alpha\beta}$) and (A$'_{grow}$) hold. Then $\mu=(\mu_t)_{t\in[0,T]}$ defined in eq:limit-sol-FPK is a solution of the FPK equation eq:limit-mu.

Theorems & Definitions (13)

  • proof
  • Example 1
  • proof
  • Theorem 4
  • proof
  • Definition 1
  • proof
  • proof
  • proof
  • Remark 1
  • ...and 3 more