The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Anshelevich, Michael. Free martingale polynomials. J. Funct. Anal. 201 (2003), no. 1, 228--261. MR1986160
  • Anshelevich, Michael. Appell polynomials and their relatives. II. Boolean theory. Indiana Univ. Math. J. 58 (2009), no. 2, 929--968. MR2514394
  • Barndorff-Nielsen, Ole E.; Thorbjørnsen, Steen. Self-decomposability and Lévy processes in free probability. Bernoulli 8 (2002), no. 3, 323--366. MR1913111
  • Benaych-Georges, Florent. Taylor expansions of $R$-transforms: application to supports and moments. Indiana Univ. Math. J. 55 (2006), no. 2, 465--481. MR2225442
  • Biane, Philippe. Processes with free increments. Math. Z. 227 (1998), no. 1, 143--174. MR1605393
  • Bożejko, Marek; Leinert, Michael; Speicher, Roland. Convolution and limit theorems for conditionally free random variables. Pacific J. Math. 175 (1996), no. 2, 357--388. MR1432836
  • Bożejko, Marek; Bryc, Włodzimierz. On a class of free Lévy laws related to a regression problem. J. Funct. Anal. 236 (2006), no. 1, 59--77. MR2227129
  • Bryc, Wlodzimierz. Classical versions of $q$-Gaussian processes: conditional moments and Bell's inequality. Comm. Math. Phys. 219 (2001), no. 2, 259--270. MR1833804
  • Laha, R. G.; Lukacs, E. On a problem connected with quadratic regression. Biometrika 47 1960 335--343. MR0121922
  • Meixner J.: Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion. Journal of the London Mathematical Society, 9, 6-13, (1934).
  • Nica, Alexandru; Speicher, Roland. Lectures on the combinatorics of free probability. London Mathematical Society Lecture Note Series, 335. Cambridge University Press, Cambridge, 2006. xvi+417 pp. ISBN: 978-0-521-85852-6; 0-521-85852-6 MR2266879
  • Saitoh, Naoko; Yoshida, Hiroaki. The infinite divisibility and orthogonal polynomials with a constant recursion formula in free probability theory. Probab. Math. Statist. 21 (2001), no. 1, Acta Univ. Wratislav. No. 2298, 159--170. MR1869728
  • Speicher, Roland. Free probability theory and non-crossing partitions. Sém. Lothar. Combin. 39 (1997), Art. B39c, 38 pp. (electronic). MR1490288
  • Takesaki, Masamichi. Conditional expectations in von Neumann algebras. J. Functional Analysis 9 (1972), 306--321. MR0303307
  • Wesołowski, Jacek. Characterizations of some processes by properties of conditional moments. Demonstratio Math. 22 (1989), no. 2, 537--556. MR1037930
  • Wesołowski, Jacek. Stochastic processes with linear conditional expectation and quadratic conditional variance. Probab. Math. Statist. 14 (1993), no. 1, 33--44. MR1267516
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.