Fluctuations of the empirical quantiles of independent Brownian motions

Stochastic Processes and their Applications

Volumn 121, Issue 3, 2011, Pages 479-514

  Swanson, Jason ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Fluctuations weak convergence; Fractional Brownian motion; Order statistics; Quantile process; Quartic variation

Indexed keywords

FRACTIONAL BROWNIAN MOTION; ORDER STATISTICS; QUANTILE PROCESS; QUARTIC VARIATION; WEAK CONVERGENCE;

BROWNIAN MOVEMENT;

EID: 78751591174     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2010.11.012     Document Type: Article

References (18)

1. Richard Arratia The motion of a tagged particle in the simple symmetric exclusion system on Z Ann. Probab. 11 2 1983 362 373
2. Patrick Billingsley Convergence of Probability Measures second ed. Wiley Series in Probability and Statistics: Probability and Statistics 1999 John Wiley & Sons Inc. New York A Wiley-Interscience Publication
3. Tomasz Bojdecki, Luis G. Gorostiza, and Anna Talarczyk Sub-fractional Brownian motion and its relation to occupation times Statist. Probab. Lett. 69 4 2004 405 419
4. Krzysztof Burdzy, Jason Swanson, A change of variable formula with it correction term, Preprint, 2008. arXiv:0802.3356v3.
5. Detlef Drr, Sheldon Goldstein, and Joel L. Lebowitz Asymptotics of particle trajectories in infinite one-dimensional systems with collisions Comm. Pure Appl. Math. 38 5 1985 573 597
6. Gerald B. Folland Real Analysis second ed. Pure and Applied Mathematics (New York) 1999 John Wiley & Sons Inc. New York Modern techniques and their applications, A Wiley-Interscience Publication
7. T.E. Harris Diffusion with collisions between particles J. Appl. Probab. 2 1965 323 338
8. M.D. Jara, and C. Landim Nonequilibrium central limit theorem for a tagged particle in symmetric simple exclusion Ann. Inst. H. Poincar Probab. Statist. 42 5 2006 567 577
9. Warren P. Johnson The curious history of Fa di Bruno's formula Amer. Math. Monthly 109 3 2002 217 234
10. Ioannis Karatzas, and Steven E. Shreve Brownian Motion and Stochastic Calculus second ed. Graduate Texts in Mathematics vol. 113 1991 Springer-Verlag New York
11. Rohini Kumar Spacetime current process for independent random walks in one dimension ALEA Lat. Am. J. Probab. Math. Stat. 4 2008 307 336
12. Anders Martin-Lf Limit theorems for the motion of a Poisson system of independent Markovian particles with high density Z. Wahrscheinlichkeitstheor. Verwandte Geb. 34 3 1976 205 223
13. Magda Peligrad, and Sunder Sethuraman On fractional Brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion ALEA Lat. Am. J. Probab. Math. Stat. 4 2008 245 255
14. Hermann Rost, and Maria Eullia Vares Hydrodynamics of a one-dimensional nearest neighbor model Particle Systems, Random Media and Large Deviations Brunswick, Maine, 1984 Contemp. Math. vol. 41 1985 Amer. Math. Soc. Providence, RI 329 342
15. Timo Sepplinen Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks Ann. Probab. 33 2 2005 759 797
16. Daniel W. Stroock Probability Theory, an Analytic View 1993 Cambridge University Press Cambridge
17. Jason Swanson Variations of the solution to a stochastic heat equation Ann. Probab. 35 6 2007 2122 2159
18. Jason Swanson Weak convergence of the scaled median of independent Brownian motions Probab. Theory Related Fields 138 12 2007 269 304