Abstract
In the first part of the paper, we consider a “random flight” process in \(R^d\) and obtain the weak limits under different transformations of the Poissonian switching times. In the second part, we construct diffusion approximations for this process and investigate their accuracy. To prove the weak convergence result, we use the approach of [15]. We consider more general model which may be called “random walk over ellipsoids in \(R^d\)”. For this model, we establish the Edgeworth-type expansion. The main tool in this part is the parametrix method [5, 7].
For the second author, this work has been funded by the Russian Academic Excellence Project ‘5–100’.
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Sincere thanks are due to the referees whose suggestions and comments have helped us to revise the article.
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Davydov, Y., Konakov, V. (2017). Random Walks in Nonhomogeneous Poisson Environment. In: Panov, V. (eds) Modern Problems of Stochastic Analysis and Statistics. MPSAS 2016. Springer Proceedings in Mathematics & Statistics, vol 208. Springer, Cham. https://doi.org/10.1007/978-3-319-65313-6_1
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DOI: https://doi.org/10.1007/978-3-319-65313-6_1
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