Multilevel Monte Carlo theta EM scheme for SDDEs with small noise
Li Tan, Chenggui Yuan
TL;DR
This paper introduces a multilevel Monte Carlo theta EM scheme tailored for stochastic differential delay equations with small noise, analyzing variance and moment properties under different Lipschitz conditions.
Contribution
It develops a modified scheme under one-sided Lipschitz conditions to ensure moment finiteness, extending the applicability of the method.
Findings
Variance of coupled paths derived under Lipschitz conditions
Modified scheme guarantees moment finiteness
Second moment estimates for coupled paths provided
Abstract
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.
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Taxonomy
TopicsStochastic processes and financial applications · Differential Equations and Numerical Methods · Fluid Dynamics and Turbulent Flows