Considering measure theory in which the semifield of positive real numbers is replaced by an idempotent semiring leads to the notion of idempotent measure introduced by Maslov. Then, idempotentâ€¦ (More)

We investigate different notions of linear independence and of matrix rank that are relevant for max-plus or tropical semirings. The factor rank and tropical rank have already received attention, weâ€¦ (More)

We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation.â€¦ (More)

We investigate the iterative behaviour of continuous order preserving subhomogeneous maps f :K â†’K, where K is a polyhedral cone in a finite dimensional vector space. We show that each bounded orbitâ€¦ (More)

We consider the asymptotics of the Perron eigenvalue and eigenvector of irreducible nonnegative matrices whose entries have a geometric dependance in a large parameter. The first term of theâ€¦ (More)

The max-plus semiring Rmax is the set Râˆª{âˆ’âˆž}, equipped with the addition (a, b) 7â†’ max(a, b) and the multiplication (a, b) 7â†’ a + b. The identity element for the addition, zero, is âˆ’âˆž, and theâ€¦ (More)

We study the optimal investment policy for an investor who has available one bank account and n risky assets modeled by log-normal diffusions. The objective is to maximize the long-run average growthâ€¦ (More)

Sylvie Detournay (INRIA and CMAP) MG for zero-sum stochastic games EMG 2010 1 / 22 DP for zero-sum stochastic games Dynamic programming equation of zero-sum two-player stochastic games v (x) = maxâ€¦ (More)

We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum, two player game problems. In particular, we set up an equivalence between theâ€¦ (More)