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All issues Volume 26 (2022) ESAIM: PS, 26 (2022) 352-377 References
Open Access
Issue
ESAIM: PS
Volume 26, 2022
Page(s) 352 - 377
DOI https://doi.org/10.1051/ps/2022009
Published online 14 September 2022
  1. M.T. Barlow, J. Pitman and M. Yor, On Walsh’s Brownian motions. Séminaire de probabilités de Strasbourg 23 (1989) 275–293. [Google Scholar]
  2. R.F. Bass, Probabilistic Techniques in Analysis. Probability and its Applications. Springer-Verlag, New York (1995). [Google Scholar]
  3. P. Brémaud, Discrete Probability Models and Methods. Vol. 78 of Probability Theory and Stochastic Modelling. Springer, Cham (2017). [CrossRef] [Google Scholar]
  4. D. Dolgopyat, M. Lenci and P. Néndori, Global observables for RW: Law of large numbers. Ann. l'Inst. Henri Poincaré — Probab. Stat. 57 (2021) 94–115. [Google Scholar]
  5. M. Freidlin and S.-J. Sheu, Diffusion processes on graphs: stochastic differential equations, large deviation principle. Probab. Theory Related Fields 116 (2000) 181–220. [CrossRef] [MathSciNet] [Google Scholar]
  6. I.I. Gikhman and A.V. Skorokhod, The Theory of Stochastic Processes I. Vol. 210 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, Berlin (1974). [Google Scholar]
  7. D.S. Grebenkov, D. Van Nguyen and J.-R. Li, Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation. J. Magn. Resonance 248 (2014) 153–163. [CrossRef] [Google Scholar]
  8. H. Hajri, Stochastic flows related to Walsh Brownian motion. Electr. J. Probab. 16 (2011) 1563–1599. [Google Scholar]
  9. H. Hajri and W. Touhami, Ito’s formula for Walsh’s Brownian motion and applications. Stat. Probab. Lett. 87 (2014) 48–53. [CrossRef] [Google Scholar]
  10. J.M. Harrison and L.A. Shepp, On skew Brownian motion. Ann. Probab. 9 (1981) 309–313. [Google Scholar]
  11. A. Iksanov and A. Pilipenko, A functional limit theorem for locally perturbed random walks. Probab. Math. Stat. 36 (2016) 353–368. [Google Scholar]
  12. A. Iksanov, A. Pilipenko and B. Povar, Functional limit theorems for random walks perturbed by positive alpha-stable jumps. To appear in Bernoulli (2021). [Google Scholar]
  13. J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes. Vol. 288 of Grundlehren der Mathematischen Wissenschaften. Springer, Berlin (2003), second edition. [CrossRef] [Google Scholar]
  14. O. Kallenberg, Foundations of Modern Probability. Probability and its Applications. Springer, New York (2002), second edition. [Google Scholar]
  15. I. Karatzas and M. Yan, Semimartingales on rays, Walsh diffusions, and related problems of control and stopping. Stoch. Process. Appl. 129 (2019) 1921–1963. [CrossRef] [Google Scholar]
  16. J. Keilson and J.A. Wellner, Oscillating Brownian motion. J. Appl. Probab. 15 (1978) 300–310. [Google Scholar]
  17. A. Lejay, On the constructions of the skew Brownian motion. Probab. Surv. 3 (2006) 413–466. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Lejay, The snapping out Brownian motion. Ann. Appl. Probab. 26 (2016) 1727–1742. [CrossRef] [MathSciNet] [Google Scholar]
  19. V. Mandrekar and A. Pilipenko, On a Brownian motion with a hard membrane. Stat. Probab. Lett. 113 (2016) 62–70. [CrossRef] [Google Scholar]
  20. R.A. Minlos and E.A. Zhizhina, Limit diffusion process for a non-homogeneous random walk on a one-dimensional lattice. Russ. Math. Surv. 52 (1997) 327–340. [CrossRef] [Google Scholar]
  21. N. Moutal and D. Grebenkov, Diffusion across semi-permeable barriers: spectral properties, efficient computation, and applications. J. Sci. Comput. 81 (2019) 1630–1654. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Nakao, On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations. Osaka J. Math. 9 (1972) 513–518. [MathSciNet] [Google Scholar]
  23. H.-L. Ngo and M. Peignée, Limit theorem for perturbed random walks. Theory Stoch. Process. 24 (2019) 61–78. [MathSciNet] [Google Scholar]
  24. D.S. Novikov, E. Fieremans, J.H. Jensen and J.A. Helpern, Random walks with barriers. Nat. Phys. 7 (2011) 508–514. [CrossRef] [PubMed] [Google Scholar]
  25. D. Paulin and D. Szász, Locally perturbed random walks with unbounded jumps. J. Stat. Phys. 141 (2010) 1116–1130. [CrossRef] [MathSciNet] [Google Scholar]
  26. V.V. Petrov, Sums of Independent Random Variables, vol. 82 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, New York (1975). [Google Scholar]
  27. A. Pilipenko, An Introduction to Stochastic Differential Equations with Reflection, vol. 11 of Lectures in Pure and Applied Mathematics. Potsdam University Press, Potsdam (2014). [Google Scholar]
  28. A. Pilipenko, A functional limit theorem for excited random walks. Electr. Commun. Prob. 22 (2017) 1–9. [Google Scholar]
  29. A. Pilipenko and Y. Pryhod’ko, Limit behavior of symmetric random walks with a membrane. Theory Probab. Math. Stat. 85 (2012) 93–105. [Google Scholar]
  30. A.Y. Pilipenko and L.A. Sakhanenko, On a limit behavior of a one-dimensional random walk with non-integrable impurity. Theory Stoch. Process. 20 (2015) 97–104. [MathSciNet] [Google Scholar]
  31. A.Y. Pilipenko and V. Khomenko, On a limit behavior of a random walk with modifications upon each visit to zero. Theory Stoch. Process. 22 (2017) 71–80. [MathSciNet] [Google Scholar]
  32. A.Y. Pilipenko and Y. E. Prikhod’ko, On the limit behavior of a sequence of Markov processes perturbed in a neighborhood of the singular point. Ukrainian Math. J. 67 (2015) 564–583. [CrossRef] [MathSciNet] [Google Scholar]
  33. A.Y. Pilipenko and Y. E. Prykhodko, Limit behavior of a simple random walk with non-integrable jump from a barrier. Theory Stoch. Process. 19 (2014) 52–61. [MathSciNet] [Google Scholar]
  34. N.I. Portenko, Generalized diffusion processes. Vol. 83 of Translations of Mathematical Monographs. American Mathematical Society, Providence, RI (1990). [Google Scholar]
  35. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. Vol. 293 of Grundlehren der Mathematischen Wissenschaften. Springer, Berlin, corrected third printing of the third edition (2005). [Google Scholar]
  36. D. Szász and A. Telcs, Random walk in an inhomogeneous medium with local impurities. J. Stat. Phys. 26 (1981) 527–537. [CrossRef] [Google Scholar]
  37. J.B. Walsh, A diffusion with a discontinuous local time. Astérisque 52 (1978) 37–45. [Google Scholar]
  38. D.A. Yarotskii, Central limit theorem for a class of nonhomogeneous random walks. Math. Notes 69 (2001) 690–695. [CrossRef] [MathSciNet] [Google Scholar]

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