Tropical geometry is a relatively recent field in mathematics and computer science, combining elements of algebraic polyhedral geometry. The scalar arithmetic its analytic part preexisted the form max-plus min-plus semiring used finite automata, nonlinear image processing, convex analysis, control, optimization, idempotent mathematics. recently emerged analysis extension several classes problem...

In this paper, we consider stochastic linear systems under the max-plus algebra. For such a system, the states are governed by the recursive equation X n = A n X n 1 U n with the initial condition X 0 = x 0 . By transforming the linear system under the max-plus algebra into a sublinear system under the usual algebra, we establish various exponential upper bounds for the tail distributions of th...