Compensated stochastic theta methods for stochastic differential equations with jumpsstar, open

• Autores: Xiaojie Wang, Siqing Gan
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 60, Nº. 9, 2010, págs. 877-887
• Idioma: inglés
• DOI: 10.1016/j.apnum.2010.04.012
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• Resumen

  • In this paper, a family of compensated stochastic theta methods (CSTM), as opposed to stochastic theta methods (STM) are proposed after the introduction of a compensated Poisson process. These methods are justified to have a strong convergence order of 1/2. Further we investigate mean-square stability of the proposed methods. For a linear test equation, we show that an extension of the deterministic A-stability property holds for CSTM, if and only if 1/2less-than-or-equals, slant?less-than-or-equals, slant1. For a general nonlinear problem, of which the drift term f has a negative one-sided Lipschitz constant and the diffusion terms g,h satisfy global Lipschitz condition, we find that backward Euler method (STM with ?=1) preserves stability under a stepsize constraint, while compensated backward Euler method (CSTM with ?=1) gives a generalization of the deterministic B-stability. Those stability results indicate that CSTM achieve superiority over STM in terms of stability.