Published

2005-07-01

HOJA BROWNIANA FRACCIONAL

FRACTIONAL BROWNIAN SHEET

Keywords:

Movimiento browniano fraccional, procesos estocásticos en dos parámetros, hoja browniana, procesos autosimilares, procesos con incrementos estacionarios (es)
Fractional Brownian motion, two-parameter stochastic processes, Brownian sheet, selfsimilary processes, stationary increments processes (en)

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Authors

  • Liliana Blanco Castañeda Universidad Nacional de Colombia
  • Johanna Garzón Merchán Universidad Nacional de Colombia
Se presenta la hoja browniana fraccional (hBf) o movimiento browniano fraccional en dos parámetros y algunas de sus propiedades importantes como son la autosimilaridad y la estacionaridad de los incrementos. Se incluyen además dos representaciones de la hBf, análogas a la representación en promedio móvil y en intervalo finito del movimiento browniano fraccional.
Fractional brownian sheet or two parameter fractional brownian motion and some important properties with selfsimilar and stationary increments are presented. Moreover, two representations for hBf analogous to moving average and on an interval representations for fractional brownian motion are included.

Hoja browniana fraccional

Fractional Brownian Sheet

LILIANA BLANCO CASTAÑEDA1, JOHANNA GARZÓN MERCHÁN2

1Departamento de Estadística, Universidad Nacional de Colombia, Bogotá. E-mail: lblancoc@unal.edu.co.
2 Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá. E-mail: mjgarzonm@unal.edu.co.

Resumen

Se presenta la hoja browniana fraccional (hBf) o movimiento browniano fraccional en dos parámetros y algunas de sus propiedades importantes como son la autosimilaridad y la estacionaridad de los incrementos. Se incluyen además dos representaciones de la hBf, análogas a la representación en pro medio móvil y en intervalo finito del movimiento browniano fraccional.

Palabras Clave: Movimiento browniano fraccional, procesos estocásticos en dos parámetros, hoja browniana, procesos autosimilares, procesos con incrementos estacionarios.

Abstract

Fractional brownian sheet or two parameter fractional brownian motion and some important properties with selfsimilar and stationary increments are presented. Moreover, two representations for hBf analogous to moving average and on an interval representations for fractional brownian motion are included.

Keywords: Fractional Brownian motion, two-parameter stochastic proces ses, Brownian sheet, selfsimilary processes, stationary increments processes.

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Referencias

1. Ayache, A. & Xiao, Y. (2004), "Asymptotic properties and Hausdorff dimension of fractional Brownian sheets".

2. Bardina, X. & Jolis, M. (2000), "Weak approximation of the Brownian sheet from a Poisson process in the plane", Bernoulli 6(4), 653- 665.

3. Bardina, X., Jolis, M. & Tudor, C. (2002), Weak Convergence to the Fractional Brownian Sheet, Universidad Autónoma de Barcelona.

4. Erraoui, M., Nualart, D. & Ouknine, Y. (2003), "Hyperbolic stochastic partial differential equations with additive fractional brownian sheet", Stochastic Dynamics 3, 121- 139.

5. Figueroa, J. (2000), Construcción de procesos autosimilares con varianza finita, Sociedad Matemática Méxicana.

6. Garzón, J. (2002), "Representación de Wong-Zakai de martingalas de dos parámetros cuadrado integrables", Universidad Nacional de Colombia, Sede Bogotá. Trabajo de grado.

7. Leger, S. (2000), Stochastic Analysis of Multifractal Signal and Parameters" Estimation, PhD thesis, Universidad de Orleans, France.

8. Nualart, D. (2003), "Stochastic integration with respect to fractional Brownian motion and applications", Contemporary Mathematics 3(39), 336.

9. Oksendal, B. & Zhang, T. (2000), "Multiparameter fractional Brownian motion and quasi-linear stochastic differential equations", Stochastics and Stochastics Reports 71, 141- 163.

10. Stroock, D. (1982), Topics in Stochastic Differential Equations, Springer Verlag.

11. Tudor, C. & Viens, F. (2003), "Itô formula and local time for the fractional Brownian sheet", Electronic Journal of Probability 8(14), 1- 31.

12. Walsh, J. (1980), "An introduction to stochastic partial differential equations", Lecture Notes in Math 1215, 239- 491.

13. Wong, E. & Zakai, M. (1974), "Martingales and stochastic integrals for processes with a dimensional parameter", Z. Wahrscheinlichkeitstheorie and Verw, Gebiete 29, 109- 122.

How to Cite

APA

Blanco Castañeda, L. and Garzón Merchán, J. (2005). HOJA BROWNIANA FRACCIONAL. Revista Colombiana de Estadística, 28(2), 193–205. https://revistas.unal.edu.co/index.php/estad/article/view/28878

ACM

[1]
Blanco Castañeda, L. and Garzón Merchán, J. 2005. HOJA BROWNIANA FRACCIONAL. Revista Colombiana de Estadística. 28, 2 (Jul. 2005), 193–205.

ACS

(1)
Blanco Castañeda, L.; Garzón Merchán, J. HOJA BROWNIANA FRACCIONAL. Rev. colomb. estad. 2005, 28, 193-205.

ABNT

BLANCO CASTAÑEDA, L.; GARZÓN MERCHÁN, J. HOJA BROWNIANA FRACCIONAL. Revista Colombiana de Estadística, [S. l.], v. 28, n. 2, p. 193–205, 2005. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/28878. Acesso em: 17 jan. 2025.

Chicago

Blanco Castañeda, Liliana, and Johanna Garzón Merchán. 2005. “HOJA BROWNIANA FRACCIONAL”. Revista Colombiana De Estadística 28 (2):193-205. https://revistas.unal.edu.co/index.php/estad/article/view/28878.

Harvard

Blanco Castañeda, L. and Garzón Merchán, J. (2005) “HOJA BROWNIANA FRACCIONAL”, Revista Colombiana de Estadística, 28(2), pp. 193–205. Available at: https://revistas.unal.edu.co/index.php/estad/article/view/28878 (Accessed: 17 January 2025).

IEEE

[1]
L. Blanco Castañeda and J. Garzón Merchán, “HOJA BROWNIANA FRACCIONAL”, Rev. colomb. estad., vol. 28, no. 2, pp. 193–205, Jul. 2005.

MLA

Blanco Castañeda, L., and J. Garzón Merchán. “HOJA BROWNIANA FRACCIONAL”. Revista Colombiana de Estadística, vol. 28, no. 2, July 2005, pp. 193-05, https://revistas.unal.edu.co/index.php/estad/article/view/28878.

Turabian

Blanco Castañeda, Liliana, and Johanna Garzón Merchán. “HOJA BROWNIANA FRACCIONAL”. Revista Colombiana de Estadística 28, no. 2 (July 1, 2005): 193–205. Accessed January 17, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/28878.

Vancouver

1.
Blanco Castañeda L, Garzón Merchán J. HOJA BROWNIANA FRACCIONAL. Rev. colomb. estad. [Internet]. 2005 Jul. 1 [cited 2025 Jan. 17];28(2):193-205. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/28878

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