Boundary preserving semi-analytical numerical algorithms for stochastic differential equations
Esteban Moro and Henri Schurz
SIAM Journal of Scientific Computation, Volume 29 Issue 4, Pages 1525-1549 (2007) [pdf]
Construction of splitting-step methods and properties of related non-negativity andboundary preserving numerical algorithms for solving stochastic differential equations (SDEs) of Ito-type are discussed. We present convergence proofs for a newly designed splitting-step algorithm and simulation studies for numerous numerical examples ranging from stochastic dynamics occurring in asset pricing theory in mathematical finance (SDEs of CIR and CEV models) to measure-valued diffusion and superBrownian motion (SPDEs) as met in biology and physics.