Law of large numbers for a general system of stochastic differential equations with global interaction

A model for the activities of N agents in an economy is presented as the solution to a system of stochastic differential equations with stochastic coefficients, driven by general semimartingales and displaying weak global interaction. We demonstrate a law of large numbers for the empirical measures belonging to the systems of processes as the number of agents goes to infinity under a weak convergence hypothesis on the triangular array of starting values, coefficients and driving semimartingales which induces the systems of equations. Further it is shown that the limit can be uniquely characterized as the weak solution to a further (nonlinear) stochastic differential equation.