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The local linearization scheme for nonlinear diffusion models with discontinuous coefficients

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  • Stramer, O.

Abstract

The local linearization scheme, defined in Shoji and Ozaki [1997, J. Time Ser. Anal. 18, 485-506] for diffusions with smooth coefficients, is studied under some regularity conditions when the coefficients are not necessarily continuous. It is shown that the local scheme converges weakly to the diffusion itself. These results are applied to continuous-time threshold autoregressive moving-average processes and multi-dimensional continuous-time threshold AR models.

Suggested Citation

  • Stramer, O., 1999. "The local linearization scheme for nonlinear diffusion models with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 249-256, April.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:3:p:249-256
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    References listed on IDEAS

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    1. R. Biscay & J. Jimenez & J. Riera & P. Valdes, 1996. "Local Linearization method for the numerical solution of stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 631-644, December.
    2. Isao Shoji & Tohru Ozaki, 1997. "Comparative study of estimation methods for continuous time stochastic processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 485-506, September.
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    Cited by:

    1. H. A. Mardones & C. M. Mora, 2020. "First-Order Weak Balanced Schemes for Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 833-852, June.

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