Optimal sampling design for global approximation of jump diffusion SDEs under jump commutativity condition

Prelegent(ci)

Paweł Przybyłowicz

Afiliacja

AGH Kraków

Termin

21 stycznia 2016 10:00

Pokój

p. 5840

Seminarium

Seminarium Zakładu Analizy Numerycznej

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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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