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    Adaptive weak approximation of reflected and stopped diffusions

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    Type
    Article
    Authors
    Bayer, Christian
    Szepessy, Anders
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Stochastic Numerics Research Group
    Date
    2010-01
    Permanent link to this record
    http://hdl.handle.net/10754/561620
    
    Metadata
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    Abstract
    We study the weak approximation problem of diffusions, which are reflected at a subset of the boundary of a domain and stopped at the remaining boundary. First, we derive an error representation for the projected Euler method of Costantini, Pacchiarotti and Sartoretto [Costantini et al., SIAM J. Appl. Math., 58(1):73-102, 1998], based on which we introduce two new algorithms. The first one uses a correction term from the representation in order to obtain a higher order of convergence, but the computation of the correction term is, in general, not feasible in dimensions d > 1. The second algorithm is adaptive in the sense of Moon, Szepessy, Tempone and Zouraris [Moon et al., Stoch. Anal. Appl., 23:511-558, 2005], using stochastic refinement of the time grid based on a computable error expansion derived from the representation. Regarding the stopped diffusion, it is based in the adaptive algorithm for purely stopped diffusions presented in Dzougoutov, Moon, von Schwerin, Szepessy and Tempone [Dzougoutov et al., Lect. Notes Comput. Sci. Eng., 44, 59-88, 2005]. We give numerical examples underlining the theoretical results. © de Gruyter 2010.
    Citation
    Bayer, C., Szepessy, A., & Tempone, R. (2010). Adaptive weak approximation of reflected and stopped diffusions. Monte Carlo Methods and Applications, 16(1), 1–67. doi:10.1515/mcma.2010.001
    Publisher
    Walter de Gruyter GmbH
    Journal
    Monte Carlo Methods and Applications
    DOI
    10.1515/MCMA.2010.001
    ae974a485f413a2113503eed53cd6c53
    10.1515/MCMA.2010.001
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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