Accuracy of discrete approximation for integral functionals of Markov processes

2015/07/31 by I. Ganychenko, Iurii Ganychenko, Victoria Knopova +6
Mathematics · #60H07 #60H35 #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #advanced mathematical theories #math.PR #msc:60H07 #msc:60H35

paper · pdf · doi:10.48550/arxiv.1507.08983

arxiv created 2015/07/31 · openalex publication_date 2015/07/31 · arxiv updated 2015/08/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in t and the derivative has an integrable upper bound of a certain type, we derive the accuracy rates for strong and weak approximations of the functionals by Riemannian sums. Some examples are provided.

Citations

• Asymptotic estimates of multi-dimensional stable densities and their applications
• Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view

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