publication . Preprint . Article . 2010

Locally Perturbed Random Walks with Unbounded Jumps

Daniel Paulin; Domokos Szász;
Open Access English
  • Published: 29 Oct 2010
Abstract
Comment: 16 pages
Subjects
arXiv: Mathematics::Probability
free text keywords: Mathematics - Probability, 60G50, 60J65, Mathematical Physics, Statistical and Nonlinear Physics, Mathematical analysis, Brownian motion, Infinite horizon, Scaling, Binary logarithm, Weak convergence, Convergence (routing), Jump, Mathematics, Random walk
20 references, page 1 of 2

1. Bleher, P. M.: Statistical Properties of Two-Dimensional Periodic Lorentz Gas with Infinite Horizon. J. of Stat. Physics, 66(1):315-373, 1992. [OpenAIRE]

2. Chernov, N. and Dolgopyat, D.: Hyperbolic billiards and statistical physics Proc. of International Congress of Mathematicians (Madrid, Spain, August 2006), Vol. II, Euro. Math. Soc., Zurich, 2006, pp. 1679-1704.

3. Chernov, N., and Dolgopyat, D.: Anomalous current in periodic Lorentz gases with infinite horizon, Uspekhi Mat. Nauk, 64:4 (2009), 73-124 (in Russian), Russ. Math. Surveys, 64 (2009) 651-699 [OpenAIRE]

4. Chernov, N., and Dolgopyat, D.: Lorentz gas with thermostatted walls, pp. 50, submitted

5. Dolgopyat, D., Szász, D. and Varjú, T.: Limit Theorems for Locally Perturbed Planar Lorentz Processes, Duke Math. Journal, 148: 459-499, 2009

6. Dvoretzky, A. and Erdős, P.: Some problems on random walk in space. Proc. 2nd Berkeley Sympos. Math. Statis. Probab., pp. 353-367 (1951) [OpenAIRE]

7. Gnedenko, B.V. and Kolmogorov, A.N.: Limit distributions for sums of independent random variables. Revised Edition (1968), Translated by K.L.Chung. Afterword: J. L. Doob. Addison-Wesley series in statistics. ASIN: B000WSX412

8. Harrison, J. M. and Shepp, L. A. On Skew Brownian Motion Ann. Probab. Volume 9, Number 2 (1981), 309-313.

9. Ibragimov, I. A. and Linnik, Yu. V.: Independent and Stationary Sequences of Random Variables 1971 Wolters-Noordhoff Publishing Groningen

10. Lawler, G. F. and Limic, V.: Random walk: a modern introduction. To be published by Cambridge University Press. Electronic version available at http://www.math.uchicago.edu/∼lawler/srwbook.pdf.

11. Lindvall, T.: Weak convergence of probability measures and random functions in the function space D[0, ∞) J. Apl. Probab. 10 (1973), 109-121 [OpenAIRE]

12. Marklof, J. and Strömbergsson, A.: Kinetic transport in the two-dimensional periodic Lorentz gas, Nonlinearity 21 (2008), 1413-1422. [OpenAIRE]

13. Rvaceva, E. On the domains of attraction of multidimensional distributions, Selected Transl. Math. Stat. Prob., 2 (1962), 183-207.

14. Skorokhod, A. V.: Limit Theorems for Stochastic Processes Theory Probab. Appl. 1, 261 (1956)

15. Spitzer, F.: Principles of Random Walk, 2nd edition, Sringer-Verlag,1976, ISBN-10: 0387951547, ISBN-13: 978-0387951546

20 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Article . 2010

Locally Perturbed Random Walks with Unbounded Jumps

Daniel Paulin; Domokos Szász;