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.