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Random Walks in Nonhomogeneous Poisson Environment

  • Youri Davydov
  • Valentin KonakovEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 208)

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].

Keywords

Random walks Random flights Random nonhomogeneous environment Diffusion approximation Parametrix method 

Notes

Acknowledgements

Sincere thanks are due to the referees whose suggestions and comments have helped us to revise the article.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Saint Petersburg State UniversitySaint PetersburgRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia

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