Convergencia de procesos aleatorios unidimensionales

Autores/as

DOI:

https://doi.org/10.21754/iecos.v24i2.2005

Palabras clave:

Distancia de Wasserstein, Proceso aleatorio, Asociado positivo

Resumen

En este trabajo desenvolvemos extensivamente algunos de los resultados obtenidos en la referencia (Cioletti et al., 2017). Usamos la distancia de Wasserstein para obtener algunos teoremas del tipo limite central para procesos aleatorios unidimensionales que tienen dependencia asociada positiva.

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Citas

Ambrosio, L. (2003). Lecture Notes on Optimal Transport Problems. In: Ambrosio, L., Deckelnick, K., Dziuk, G., Mimura, M., Solonnikov, V. A., Soner, H. M., & Ambrosio, L. (Eds.), Mathematical Aspects of Evolving Interfaces (pp. 1-52). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-39189-0_1

Barlow, R. E., & Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. Holt, Rinehart and Winston. https://apps.dtic.mil/sti/citations/ADA006399

Bickel, P. J., & Freedman, D. A. (1981). Some asymptotic theory for the bootstrap. The annals of statistics, 9(6), 1196-1217. https://doi.org/10.1214/aos/1176345637

Birkel, T. (1988). Moment bounds for associated sequences. The annals of Probability, 16(3), 1184-1193. https://www.jstor.org/stable/2244116

Cioletti, L., Dorea, C. C. Y., & Vila, R. (2017). Limit Theorems in Mallows Distance for Processes with Gibssian Dependence. arXiv.

https://doi.org/10.48550/arXiv.1701.03747

Dorea, C. C., & Ferreira, D. B. (2012). Conditions for equivalence between Mallows distance and convergence to stable laws. Acta Mathematica Hungarica, 134(1-2), 1-11. https://doi.org/10.1007/s10474-011-0101-7

Esary, J. D., Proschan, F., & Walkup, D. W. (1967). Association of random variables, with applications. The Annals of Mathematical Statistics, 38(5), 1466-1474. https://doi.org/10.1214/aoms/1177698701

Gabriel, R. V. (2017). Representações gráficas para sistemas de spins com presença de campo externo: algumas relações em teoria de probabilidades [Tese para obtenção do grau de Doutor em Matemática]. Universidade de Brasília. Instituto de Ciências Exatas. Departamento de Matemática. http://icts.unb.br/jspui/handle/10482/22471

Gray, R. M. (2009). Probability, random processes, and ergodic properties. Springer. https://doi.org/10.1007/978-1-4419-1090-5

Jordan, R., Kinderlehrer, D., & Otto, F. (1998). The variational formulation of the Fokker--Planck equation. SIAM journal on mathematical analysis, 29(1), 1-17. https://doi.org/10.1137/S0036141096303359

Kantorovic ̌, L. V., Rubins ̌tei ̌n, G. S ̌. (1958). On a space of completely additive functions. Vestnik Leningrad University, 13, 52-59.

Mallows, C. L. (1972). A note on asymptotic joint normality. The Annals of Mathematical Statistics, 43(2), 508-515. https://www.jstor.org/stable/2239988

Newman, C. M. (1980). Normal fluctuations and the FKG inequalities. Communications in Mathematical Physics, 74(2), 119-128. https://doi.org/10.1007/BF01197754

Newman, C. M., & Wright, A. L. (1981). An invariance principle for certain dependent sequences. The Annals of Probability, 9(4), 671-675.

https://doi.org/10.1214/aop/1176994374

Oliveira, P. E. (2012). Asymptotics for associated random variables. Springer Science & Business Media.

Otto, F. (2001). The geometry of dissipative evolution equations: the porous medium equation. Communications in Partial Differential Equations, 26(1-2), 101-174 https://doi.org/10.1081/PDE-100002243

Pitt, L. D. (1982). Positively correlated normal variables are associated. The Annals of Probability, 10(2), 496-499. https://www.jstor.org/stable/2243445

Rachev, S. T., & Rüschendorf, L. (1998). Mass Transportation Problems: Volume I: Theory. Springer Science & Business Media.

Shorack, G. R., & Wellner, J. A. (2009). Empirical processes with applications to statistics. Society for Industrial and Applied Mathematics.

https://epubs.siam.org/doi/pdf/10.1137/1.9780898719017.bm

Sommerfeld, M., & Munk, A. (2018). Inference for empirical Wasserstein distances on finite spaces. Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(1), 219-238. https://doi.org/10.1111/rssb.12236

Vaserstein, L. N. (1969). Markov processes over denumerable products of spaces, describing large systems of automata. Problemy Peredachi Informatsii, 5(3), 64-72. https://www.mathnet.ru/eng/ppi1811

Villani, C. (2003). Topics in optimal transportation. OR/MS Today, 30(3), 66-67. https://link.gale.com/apps/doc/A104669453/AONE?u=anon~6226aa1c&sid=googleScholar&xid=2585334e

Villani, C. (2009). Optimal transport: old and new. Springer. https://doi.org/10.1007/978-3-540-71050-9

Yeh, J. (2006). Real Analysis: Theory of Measure and Integration. World Scientific.

Publicado

2023-12-31

Cómo citar

Vila Gabriel, R. (2023). Convergencia de procesos aleatorios unidimensionales. Revista IECOS, 79–100. https://doi.org/10.21754/iecos.v24i2.2005

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Sección

Artículos de Investigación