publication . Preprint . Article . Doctoral thesis . Other literature type . 2015

On a functional contraction method

Neininger, Ralph; Sulzbach, Henning;
Open Access English
  • Published: 01 Jul 2015
  • Country: Germany
Comment: Published at in the Annals of Probability ( by the Institute of Mathematical Statistics (
free text keywords: Mathematics - Probability, Computer Science - Data Structures and Algorithms, Functional limit theorem, contraction method, recursive distributional equation, Zolotarev metric, Donsker’s invariance principle, 60F17, 68Q25, 60G18, 60C05, Mathematical analysis, Stochastic process, Donsker's theorem, Limit of a function, Recursion, Contraction mapping, Mathematics, Combinatorics, Probabilistic analysis of algorithms, Continuous function, ddc:510
31 references, page 1 of 3

[1] Aldous, D. (1994) Recursive self-similarity for random trees, random triangulations and Brownian excursion. Ann. Probab. 22, 527-545. [OpenAIRE]

[2] Barbour, A.D. (1990) Stein's method for diffusion approximations. Probab. Theory Related Fields 84, 297-322. [OpenAIRE]

[3] Barbour, A.D. and Janson, S. (2009) A functional combinatorial central limit theorem. Electron. J. Probab. 14, 2352-2370.

[4] Bentkus, V.Yu. and Rachkauskas, A. (1984) Estimates of distances between sums of independent random elements in Banach spaces. Teor. Veroyatnost. i Primenen. 29, 49-64.

[5] Billingsley, P. (1999) Convergence of probability measures. Second edition. Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York.

[6] Broutin, N., Neininger, R. and Sulzbach, H. (2012) A limit process for partial match queries in random quadtrees. Preprint available [OpenAIRE]

[7] Cartan, H. (1971) Differential calculus. Hermann, Paris; Houghton Mifflin Co., Boston, Mass.

[8] Dieudonne´, J. (1960) Foundations of modern analysis. Pure and Applied Mathematics, Vol. X. Academic Press, New York.

[9] Donsker, M.D. (1951) An invariance principle for certain probability limit theorems. Mem. Amer. Math. Soc. 6, 12 pp.

[10] Drmota, M., Janson, S. and Neininger, R. (2008) A functional limit theorem for the profile of search trees. Ann. Appl. Probab. 18, 288-333.

[11] Eickmeyer, K. and Ru¨schendorf, L. (2007) A limit theorem for recursively defined processes in Lp. Statist. Decisions 25, 217-235.

[12] Fre´chet, M. (1915) Sur les fonctionelles biline´aires. Trans. Amer. Math. Soc. 16, 215-234.

[13] Gine´, E. and Leon, J.R. (1980) On the central limit theorem in Hilbert space. Stochastica 4, 43-71.

[14] Janson, S. and Neininger, R. (2008) The size of random fragmentation trees. Probab. Theory Related Fields 142, 399-442.

[15] Ledoux, M. and Talagrand, M. (1991) Probability in Banach spaces. Isoperimetry and processes. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Vol. 23. Springer-Verlag, Berlin. [OpenAIRE]

31 references, page 1 of 3
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Article . Doctoral thesis . Other literature type . 2015

On a functional contraction method

Neininger, Ralph; Sulzbach, Henning;