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Local Linear Approximations of Jump Diffusion Processes

  • J. C. Jimenez (a1) and F. Carbonell (a1)

Abstract

Local linear approximations have been the main component in the construction of a class of effective numerical integrators and inference methods for diffusion processes. In this note, two local linear approximations of jump diffusion processes are introduced as a generalization of the usual ones. Their rate of uniform strong convergence is also studied.

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Copyright

Corresponding author

Postal address: Departamento de Sistemas Adaptativos, Instituto de Cibernética, Matemática y Física, Calle 15, No. 551, Vedado, La Habana 4, C.P. 10400, Cuba.
∗∗ Email address: jcarlos@icmf.inf.cu
∗∗∗ Email address: felix@icmf.inf.cu

Footnotes

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Partially supported by the research grant 03-059 RG/MATHS/LA from the ThirdWorld Academy of Science.

Footnotes

References

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[2] Jimenez, J. C. (2002). A simple algebraic expression to evaluate the local linearization schemes for stochastic differential equations. Appl. Math. Lett. 15, 775780.
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[4] Jimenez, J. C., Shoji, I. and Ozaki, T. (1999). Simulation of stochastic differential equations through the local linearization method. A comparative study. J. Statist. Phys. 94, 587602.
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[8] Ozaki, T. (1985). Nonlinear time series models and dynamical systems. In Time Series in the Time Domain (Handbook Statist. 5), eds Hannan, E. J. et al., North-Holland, Amsterdam, pp. 2583.
[9] Ozaki, T. (1992). A bridge between nonlinear time series models and nonlinear stochastic dynamical systems: a local linearization approach. Statistica Sinica 2, 113135.
[10] Prakasa-Rao, B. L. S. (1999). Statistical Inference for Diffussion Type Processes. Oxford University Press.
[11] Protter, P. (1990). Stochastic Integration and Differential Equations. Springer, Berlin.
[12] Schurz, H. (2002). Numerical analysis of stochastic differential equations without tears. In Handbook of Stochastic Analysis and Applications (Statist. Textbook Monogr. 163), eds Kannan, D. and Lakahmikamtham, V., Marcel Dekker, New York, pp. 237359.
[13] Shoji, I. and Ozaki, T. (1997). Comparative study of estimation methods for continuous time stochastic processes. J. Time Series Anal. 18, 485506.
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Local Linear Approximations of Jump Diffusion Processes

  • J. C. Jimenez (a1) and F. Carbonell (a1)

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