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

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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.

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