Lotka-Volterra with randomly fluctuating environments: a full   description
  In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Benam and Lobry established that randomly switching between two environments that are both favorable to the same species may lead to four different regimes: almost sure extinction of one of the two species, random extinction of one species or the other and persistence of both species. Our purpose here is to provide a complete description of the model. In particular, we show that any couple of environments may lead to the four different behaviours of the stochastic process depending on the jump rates. 
Florent Malrieu (LMPT, FRDP), Tran Hoa Phu (LMPT)
math.PR