Maslov idempotent probability calculus. II

The study of Bellman–Maslov processes has lead to new advances in the understanding of optimal control problems and of its relation to the study of Hamilton–Jacobi differential equations. The aim of this work is to show that idempotent calculus yields a natural and general probabilistic line of thought for studying such equations. Some new results relating to the long-time behavior of the solution of a class of Hamilton–Jacobi differential equations can be regarded as a $(\max,+)$-version of the law of large numbers and the central limit theorem. The applications to some evolution equation arising in mathematical morphology are also discussed.