Jump-Adapted Strong Approximations
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This chapter describes jump-adapted strong schemes. The term jump-adapted refers to the time discretizations used to construct these schemes. These discretizations include all jump times generated by the Poisson jump measure. The form of the resulting schemes is much simpler than that of the regular schemes presented in Chaps. 6 and 7 which are based on regular time discretizations. The idea of jump-adapted time discretization goes back to Platen (1982a). It appeared later in various literature, for instance, Maghsoodi (1996). Jump-adapted schemes are not very efficient for SDEs driven by a Poisson measure with a high total intensity. In this case, regular schemes would usually be preferred. Some of the results of this chapter can be found in Bruti-Liberati et al. (2006) and in Bruti-Liberati & Platen (2007b). Results presented already in Kloeden & Platen (1999) and Chap. 5 are employed in the following when approximating the diffusion part of the solution of an SDE.
KeywordsStrong Convergence Time Step Size Discretization Error Euler Scheme Jump Time
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- Kloeden, P. E. & Platen, E. (1999). Numerical Solution of Stochastic Differential Equations, Vol. 23 of Appl. Math., Springer. Third printing, (first edition (1992)). Google Scholar