Construction of positivity preserving numerical schemes for multidimensional stochastic differential equations

2013/10/06 by Halidias, Nikolaos
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1310.1581

Abstract

In this note we work on the construction of positive preserving numerical schemes for systems of stochastic differential equations. We use the semi discrete idea that we have proposed before proposing now a numerical scheme that preserves positivity on multidimensional stochastic differential equations converging strongly in the mean square sense to the true solution.

Related

• On the numerical solution of some nonlinear stochastic differential\n equations using the semi-discrete method
• Positivity-preserving schemes for some nonlinear stochastic PDEs
• Strong convergence rate of positivity-preserving truncated Euler--Maruyama method for multi-dimensional stochastic differential equations with positive solutions
• Unconditionally positivity-preserving explicit order-one strong approximations of financial SDEs with non-Lipschitz coefficients
• Preserving invariant domains and strong approximation of stochastic differential equations