Multilevel Monte Carlo theta EM scheme for SDDEs with small noise
This work provides a numerical method for a specific class of stochastic differential equations, but the contribution is incremental as it extends existing multilevel Monte Carlo techniques to a new setting.
The paper develops a multilevel Monte Carlo theta EM scheme for stochastic differential delay equations with small noise, deriving variance estimates under Lipschitz and one-sided Lipschitz conditions.
In this paper, a multilevel Monte Carlo theta EM scheme is provided for stochastic differential delay equations with small noise. Under a global Lipschitz condition, the variance of two coupled paths is derived. Then, the global Lipschitz condition is replaced by one-sided Lipschitz condition, in order to guarantee the moment finiteness of numerical scheme, a modified multilevel Monte Carlo theta EM scheme is put forward and the second moment of two coupled paths is estimated.