|
|
|
Ñïèñîê ëèòåðàòóðû
|
|
|
1. |
Allaway W. R., “On finding the distribution function for an orthogonal polynomial set”, Pacific J. Math., 49 (1973), 305–310 |
2. |
Allaway W. R., The identification of a class of orthogonal polynomial sets, Ph. D. thesis, University of Alberta, Ann Arbor, MI, 1972 |
3. |
Anshelevich M., “Bochner–Pearson-type characterization of the free Meixner class”, Adv. in Appl. Math., 46 (2011), 25–45, arXiv: 0909.1097 |
4. |
Anshelevich M., “Free martingale polynomials”, J. Funct. Anal., 201 (2003), 228–261, arXiv: math.CO/0112194 |
5. |
Aptekarev A. I., “Asymptotic properties of polynomials orthogonal on a system of contours, and periodic moments of Toda lattices”, Math. USSR Sb., 53 (1986), 233–260 |
6. |
Askey R., Wilson J., Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc., 54, no. 319, 1985, iv+55 pp. |
7. |
Chihara T. S., An introduction to orthogonal polynomials, Mathematics and its Applications, 13, Gordon and Breach Science Publishers, New York, 1978 |
8. |
Cohen J. M., Trenholme A. R., “Orthogonal polynomials with a constant recursion formula and an application to harmonic analysis”, J. Funct. Anal., 59 (1984), 175–184 |
9. |
Damanik D., Killip R., Simon B., “Perturbations of orthogonal polynomials with periodic recursion coefficients”, Ann. of Math. (2), 171 (2010), 1931–2010, arXiv: math.SP/0702388 |
10. |
Dette H., Reuther B., Studden W. J., Zygmunt M., “Matrix measures and random walks with a block tridiagonal transition matrix”, SIAM J. Matrix Anal. Appl., 29 (2007), 117–142 |
11. |
Feller W., An introduction to probability theory and its applications, v. 1, John Wiley & Sons, Inc., New York, 1967 |
12. |
Feller W., “On second order differential operators”, Ann. of Math. (2), 61 (1955), 90–105 |
13. |
Foster F. G., “On the stochastic matrices associated with certain queuing processes”, Ann. Math. Stat., 24 (1953), 355–360 |
14. |
Geronimus J. L., “On a set of polynomials”, Ann. of Math. (2), 31 (1930), 681–686 |
15. |
Geronimus J. L., “On some equations in finite differences and the corresponding systems of orthogonal polynomials”, Zap. Mat. Otdel. Fiz.-Mat. Fak. i Kharkov. Mat. Obshch., 25 (1957), 87–100 (in Russian) |
16. |
Good I. J., “Random motion and analytic continued fractions”, Proc. Cambridge Philos. Soc., 54 (1958), 43–47 |
17. |
Grünbaum F. A., “Random walks and orthogonal polynomials: some challenges”, Probability, geometry and integrable systems, Math. Sci. Res. Inst. Publ., 55, Cambridge Univ. Press, Cambridge, 2008, 241–260, arXiv: math.PR/0703375 |
18. |
Harris T. E., “First passage and recurrence distributions”, Trans. Amer. Math. Soc., 73 (1952), 471–486 |
19. |
Hodges Jr. J. L., Rosenblatt M., “Recurrence-time moments in random walks”, Pacific J. Math., 3 (1953), 127–136 |
20. |
Ismail M. E. H., Masson D. R., Letessier J., Valent G., “Birth and death processes and orthogonal polynomials”, Orthogonal Polynomials (Columbus, OH, 1989), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 294, Kluwer Acad. Publ., Dordrecht, 1990, 229–255 |
21. |
Kac M., “Random walk and the theory of Brownian motion”, Amer. Math. Monthly, 54 (1947), 369–391 |
22. |
Karlin S., A first course in stochastic processes, Academic Press, New York, 1966 |
23. |
Karlin S., McGregor J., “Random walks”, Illinois J. Math., 3 (1959), 66–81 |
24. |
Ledermann W., Reuter G. E. H., “Spectral theory for the differential equations of simple birth and death processes”, Philos. Trans. Roy. Soc. London. Ser. A., 246 (1954), 321–369 |
25. |
McKean Jr. H. P., “Elementary solutions for certain parabolic partial differential equations”, Trans. Amer. Math. Soc., 82 (1956), 519–548 |
26. |
Saitoh N., Yoshida H., “The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory”, Probab. Math. Stat., 21 (2001), 159–170 |
27. |
Sodin S., “Random matrices, nonbacktracking walks, and orthogonal polynomials”, J. Math. Phys., 48 (2007), 123503, 21 pp., arXiv: math-ph/0703043 |
28. |
Szeg{ö} G., Orthogonal polynomials, American Mathematical Society, Colloquium Publications, 23, 4th ed., Amer. Math. Soc., Providence, R.I., 1975 |
29. |
van Doorn E. A., Schrijner P., “Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes”, J. Austral. Math. Soc. Ser. B, 37 (1995), 121–144 |
30. |
van Doorn E. A., Schrijner P., “Ratio limits and limiting conditional distributions for discrete-time birth-death processes”, J. Math. Anal. Appl., 190 (1995), 263–284 |