A higher-order approximation method for jump-diffusion SDEs with a discontinuous drift coefficient

Przybyłowicz, Paweł; Schwarz, Verena; Szölgyenyi, Michaela

doi:10.1016/j.jmaa.2024.128319

Journal of Mathematical Analysis and Applications

2024

DOI: 10.1016/j.jmaa.2024.128319

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A higher-order approximation method for jump-diffusion SDEs with a discontinuous drift coefficient

Paweł Przybyłowicz,

Verena Schwarz,

Michaela Szölgyenyi

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2024

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Cited by 4 publications

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Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

Przybyłowicz,

Schwarz,

Szölgyenyi

2024

Bit Numer Math

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In this paper sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift are proven. The approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes is studied and lower error bounds of order 3/4 for both classes of approximation schemes are provided. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.

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Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

Przybyłowicz,

Schwarz,

Szölgyenyi

2024

Bit Numer Math

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Adaptive step-size control for global approximation of SDEs driven by countably dimensional Wiener process

Stępień

2023

Numer Algor

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In this paper, we deal with the global approximation of solutions of stochastic differential equations (SDEs) driven by countably dimensional Wiener process. Under certain regularity conditions imposed on the coefficients, we show lower bounds for exact asymptotic error behaviour. For that reason, we analyse separately two classes of admissible algorithms: based on equidistant, and possibly not equidistant meshes. Our results indicate that in both cases, decrease of any method error requires significant increase of the cost term, which is illustrated by the product of cost and error diverging to infinity. This is, however, not visible in the finite-dimensional case. In addition, we propose an implementable, path-independent Euler algorithm with adaptive step-size control, which is asymptotically optimal among algorithms using specified truncation levels of the underlying Wiener process. Our theoretical findings are supported by numerical simulation in Python language.

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On the complexity of strong approximation of stochastic differential equations with a non-Lipschitz drift coefficient

Müller-Gronbach,

Yaroslavtseva

2024

Journal of Complexity

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A higher-order approximation method for jump-diffusion SDEs with a discontinuous drift coefficient

Cited by 4 publications

References 46 publications

Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

Adaptive step-size control for global approximation of SDEs driven by countably dimensional Wiener process

On the complexity of strong approximation of stochastic differential equations with a non-Lipschitz drift coefficient

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