SPDEs on narrow domains and on graphs: an asymptotic approach
  We introduce here a class of stochastic partial differential equations defined on a graph and we show how they are obtained as the limit of suitable stochastic partial equations defined in a narrow channel, as the width of the channel goes to zero. To our knowledge, this is the first time an SPDE on a graph is studied. 
Sandra Cerrai and Mark Freidlin
math.PR