Numerical solution stability of general stochastic differential equation

Abstract

Stochastic differential equation has accumulated a large number of bases in numeral analysis over decades of development. It can accurately and truly reflect some development rules in the fields such as economics, physics and astronomy when being applied in practice. Stability of numeral solution is the key in numerical analysis of stochastic differential equation. In this study, the stability of numeral solution of stochastic differential equation was discussed and verified. Nonlinear stochastic equation was solved using stochastic-θ method under general decay rate, and two sufficient conditions were proposed for the obtained numerical solutions. It was verified that the numeral solution obtained using stochastic-θ method was p-th moment Φ(t)-stable and almost surely Φ(t)-stable under the sufficient conditions.

Keywords:

• Stochastic differential equation
• General decay rate
• Random θ method
• Stability