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Optimal sampling design for global approximation of jump diffusion SDEs under jump commutativity condition
- Speaker(s)
- Paweł Przybyłowicz
- Affiliation
- AGH Kraków
- Date
- Jan. 21, 2016, 10 a.m.
- Room
- room 5840
- Seminar
- Seminar of Numerical Analysis Group
Abstract:
We study minimal asymptotic errors for strong global approximation of SDEs driven by two independent processes: a nonhomogeneous Poisson process N and a Wiener process W. We assume that the jump and diffusion coefficients of the underlying SDE satisfy the jump commutativity condition. We consider two cases of sampling of N and W: equidistant and nonequidistant. In both cases, we show that the minimal error tends to zero like $C n^{−1/2}$, where C is the average in time of a local Holder constant of the solution and n is the number of evaluations of N and W. The asymptotic constant C when the equidistant sampling is used can be considerably larger than the asymptotic constant in the nonuniform sampling case. We also provide a construction of methods, based on the classical Milstein scheme, that asymptotically achieve the established minimal errors.
We study minimal asymptotic errors for strong global approximation of SDEs driven by two independent processes: a nonhomogeneous Poisson process N and a Wiener process W. We assume that the jump and diffusion coefficients of the underlying SDE satisfy the jump commutativity condition. We consider two cases of sampling of N and W: equidistant and nonequidistant. In both cases, we show that the minimal error tends to zero like $C n^{−1/2}$, where C is the average in time of a local Holder constant of the solution and n is the number of evaluations of N and W. The asymptotic constant C when the equidistant sampling is used can be considerably larger than the asymptotic constant in the nonuniform sampling case. We also provide a construction of methods, based on the classical Milstein scheme, that asymptotically achieve the established minimal errors.
