Polynomial jump-diffusions on the unit simplex
  Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit simplex under natural structural hypotheses on the jumps. As a stepping stone, we characterize well-posedness of the martingale problem for polynomial operators on general compact state spaces. 
Christa Cuchiero, Martin Larsson, and Sara Svaluto-Ferro
math.PR