A splitting-step algorithm for reflected stochastic differential equations in R+1
Computers & Mathematics with Applications
Discrete Gradient Approach to Stochastic Differential Equations with a Conserved Quantity
SIAM Journal on Numerical Analysis
High-order approximation of Pearson diffusion processes
Journal of Computational and Applied Mathematics
Computing Stochastic Traveling Waves
SIAM Journal on Scientific Computing
An Efficient Semi-Analytical Simulation for the Heston Model
Computational Economics
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Construction of splitting-step methods and properties of related nonnegativity and boundary preserving semianalytic numerical algorithms for solving stochastic differential equations (SDEs) of Itô type are discussed. As the crucial assumption, we oppose conditions such that one can decompose the original system of SDEs into subsystems for which one knows either the exact solution or its conditional transition probability. We present convergence proofs for a newly designed splitting-step algorithm and simulation studies for numerous well-known numerical examples ranging from stochastic dynamics occurring in asset pricing in mathematical finance (Cox-Ingersoll-Ross (CIR) and constant elasticity of variance (CEV) models) to measure-valued diffusion and super-Brownian motion (stochastic PDEs (SPDEs)) as met in biology and physics.