Weak convergence of Euler-Maruyama's approximation for SDEs under integrability condition
arXiv:1808.07250
Abstract
This work establishes the weak convergence of Euler-Maruyama's approximation for stochastic differential equations (SDEs) with singular drifts under the integrability condition in lieu of the widely used growth condition. This method is based on a skillful application of the dimension-free Harnack inequality. Moreover, when the drifts satisfy certain regularity conditions, the convergence rate is estimated. This method is also applicable when the diffusion coefficients are degenerate. A stochastic damping Hamiltonian system is studied as an illustrative example.
arXiv comment33 pages
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Cited by in corpus (3)
- Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
- Convergence rate of EM algorithm for SDEs under integrability condition
- Weak convergence of Euler scheme for SDEs with singular drift