G. Merlet

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math.PR2007

Cycle time of stochastic max-plus linear systems

Glenn Merlet

We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula…

math.PR2006★ 1 cited

Law of Large Numbers for products of random matrices with coefficients in the max-plus semi-ring

Glenn Merlet

We analyze the asymptotic behavior of random variables $x (n, x_0)$ defined by $x (0, x_0) = x_0$ and $x (n + 1, x_0) = A (n) x (n, x_0)$ , where $\sAn$ is a stationary and ergodic sequence of…

math.PR2006★ 3 cited

A central limit theorem for stochastic recursive sequences of topical operators

Glenn Merlet

Let $(A_{n})_{n \in N}$ be a stationary sequence of topical (i.e., isotone and additively homogeneous) operators. Let $x (n, x_{0})$ be defined by $x (0, x_{0}) = x_{0}$ and $x(n+1,x_0)=A…

math.PR2005

Limit theorems for iterated random topical operators

Glenn Merlet

Let A(n) be a sequence of i.i.d. topical (i.e. isotone and additively homogeneous) operators. Let $x (n, x_{0})$ be defined by $x (0, x_{0}) = x_{0}$ and $x (n, x_{0}) = A (n) x (n - 1, x_{0})$ . This can mo…

math.PR2004

Memory loss property for products of random matrices in the $(max, +)$ algebra

Glenn Merlet

Products of random matrices in the $(max, +)$ algebra are used as a model for a class of discrete event dynamical systems. J. Mairesse proved that such a system couples in finite t…

Cycle time of stochastic max-plus linear systems

Law of Large Numbers for products of random matrices with coefficients in the max-plus semi-ring

A central limit theorem for stochastic recursive sequences of topical operators

Limit theorems for iterated random topical operators

Memory loss property for products of random matrices in the (max,+) algebra

Memory loss property for products of random matrices in the $(max, +)$ algebra