Law of large numbers for a general system of stochastic differential equations with global interaction
A law of large numbers in the form of the weak convergence of the empirical measures on trajectories of processes forming a triangular array is deduced. Then \(n\) processes in the \(n\)th line of the array are given as the solutions of a system of ordinary stochastic differential equations derived by semimartingales with a special (``mean field'') interaction. The limit is described as the solution of another stochastic differential equation. The model is motivated consisely by possible applications in economy. The proofs are based on a special discrete time approximation of the array of processes, nontrivial estimates, and stability results of J. Jacod and J. Memin.
weak convergence of the empirical measures
ordinary stochastic differential equations
scientific article; zbMATH DE number 203261
scientific article