Espérances et majorations pour un processus de branchement spatial markovien. (Expectation and majorization for a Markov spatial branching process) (Q1111251)

For a supercritical Galton-Watson process \((Z_ n)_{n\in {\mathbb{N}}}\), \(n^{-1}Log E Z_ n\) and \(n^{-1}Log Z_ n\) have the same limit m. In the Markovian case with exponential initial population, we give here a limit for the analogue of the first expression and an overestimation - in probability - for an analogue of the second one. Two variational formulas are at stake; the second one, with constraint over action integral, allows the definition of ``presence areas''.