Path-probability density functions for semi-Markovian random walks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 4, 2007, Pages

  Flomenbom, O ^a   Silbey, R J ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GREEN'S FUNCTION; PROBABILITY DENSITY FUNCTION; Z TRANSFORMS;

LAPLACE SPACE; RANDOM WALK; RECURSION RELATION;

MARKOV PROCESSES;

EID: 34948818257     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.041101     Document Type: Article

References (42)

1. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, revised and enlarged edition (North-Holland, Amsterdam, 1992).
2. S. Redner, A Guide to First-Passage Process (Cambridge University Press, Cambridge, UK, 2001).
3. N. W. Goel and N. Richter-Dyn, Stochastic Models in Biology (Academic Press, New York, 1974).
4. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986);
5. P. G. De Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).
6. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).
7. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
8. D. R. Cox, Renewal Theory (Methuen, London, 1962).
9. C. Van Den Broeck and M. Bouten, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01020587 45, 1031 (1986).
10. V. M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016796 9, 45 (1973).
11. J. Klafter and R. Silbey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.44.55 44, 55 (1980).
12. E. W. Montroll and G. H. Weiss, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704269 6, 167 (1965).
13. H. Scher and M. Lax, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.7. 4491 7, 4491 (1973).
14. O. Flomenbom and J. Klafter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.098105 95, 098105 (2005);
15. O. Flomenbom, J. Klafter, and R. J. Silbey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.178901 97, 178901 (2006).
16. O. Flomenbom and R. J. Silbey, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2743969 127, 034103 (2007).
17. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000).
18. H. Qian and H. Wang, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10239-9 76, 15 (2006).
19. W. E. Moerner and M. Orrit, Science SCIEAS 0036-8075 10.1126/science.283. 5408.1670 283, 1670 (1999);
20. S. Weiss, Science SCIEAS 0036-8075 10.1126/science.283.5408.1676 283, 1676 (1999).
21. B. Hille, Ion Channels of Excitable Membranes (Sinauer Associates Inc., Sunderland, 2001).
22. A. Meller, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/15/17/202 15, R581 (2003).
23. X. Zhuang, Annu. Rev. Biophys. Biomol. Struct. ABBSE4 1056-8700 10.1146/annurev.biophys.34.040204.144641 34, 399 (2005).
24. H. Lu, L. Xun, and X. S. Xie, Science SCIEAS 0036-8075 10.1126/science.282.5395.1877 282, 1877 (1998).
25. L. Edman, Z. Földes-Papp, S. Wennmalm, and R. Rigler, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(99)00098-1 247, 11 (1999).
26. A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, Science SCIEAS 0036-8075 10.1126/science.283.5408.1689 283, 1689 (1999).
27. O. Flomenbom, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0409039102 102, 2368 (2005);
28. O. Flomenbom, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/j.cplett.2006. 10.060 432, 371 (2006);
29. K. Velonia, Angew. Chem., Int. Ed. ACIEF5 1433-7851 10.1002/anie. 200460625 44, 560 (2005).
30. I. Chung and M. G. Bawendi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.165304 70, 165304 (2004).
31. O. Flomenbom and R. J. Silbey, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0604546103 103, 10907 (2006).
32. W. J. Bruno, J. Yang, and J. Pearson, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0409110102 102, 6326 (2005).
33. D. R. Fredkin and J. A. Rice, J. Appl. Probab. JPRBAM 0021-9002 10.2307/3214130 23, 208 (1986).
34. O. Flomenbom, J. Klafter, and A. Szabo, Biophys. J. BIOJAU 0006-3495 10.1529/biophysj.104.055905 88, 3780 (2005);
35. O. Flomenbom and J. Klafter, Acta Phys. Pol. B APOBBB 0587-4254 36, 1527 (2005);
36. O. Flomenbom and J. Klafter, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1979489 123, 064903 (2005).
37. J. Cao, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(00)00809-5 327, 38 (2000);
38. S. Yang and J. Cao, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1521155 117, 10996 (2002);
39. J. B. Witkoskie and J. Cao, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1785783 121, 6361 (2004).
40. D. Colquhoun and A. G. Hawkes, Philos. Trans. R. Soc. London, Ser. B PTRBAE 0962-8436 10.1098/rstb.1982.0156 300, 1 (1982).
41. E. Barkai, Y. Jung, and R. Silbey, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 10.1146/annurev.physchem.55.111803.143246 55, 457 (2004).
42. F. L. H. Brown, Acc. Chem. Res. ACHRE4 0001-4842 10.1021/ar050028l 39, 363 (2006).