Stochastic Calculus for Fractional Brownian Motion and Applications

In this paper, we construct fractional Lévy processes for any parameter H ∈ (0, 1), as the generalization of the fractional Brownian motion. By using Malliavin calculus, we also define the stochastic integral for fractional Lévy processes.

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Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 12

Stochastic Processes and their Applications ◽

10.1016/s0304-4149(99)00089-7 ◽

2000 ◽

Vol 86 (1) ◽

pp. 121-139 ◽

Cited By ~ 61

Author(s):

Elisa Alòs ◽

Olivier Mazet ◽

David Nualart

Keyword(s):

Brownian Motion ◽

Fractional Brownian Motion ◽

Stochastic Calculus ◽

Hurst Parameter

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From Constructive Field Theory to Fractional Stochastic Calculus. (II) Constructive Proof of Convergence for the Lévy Area of Fractional Brownian Motion with Hurst Index $${{\alpha}\,{\in}\,(\frac{1}{8},\frac{1}{4})}$$

Annales Henri Poincaré ◽

10.1007/s00023-011-0119-y ◽

2011 ◽

Vol 13 (2) ◽

pp. 209-270 ◽

Cited By ~ 3

Author(s):

Jacques Magnen ◽

Jérémie Unterberger

Keyword(s):

Field Theory ◽

Brownian Motion ◽

Fractional Brownian Motion ◽

Stochastic Calculus ◽

Constructive Proof ◽

Hurst Index ◽

Constructive Field Theory ◽

Proof Of Convergence

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Stochastic calculus for fractional Brownian motion. I. Theory

Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) ◽

10.1109/cdc.2000.912761 ◽

2002 ◽

Cited By ~ 4

Author(s):

T.E. Duncan ◽

Y.Z. Hu ◽

B. Pasik-Duncan

Keyword(s):

Brownian Motion ◽

Fractional Brownian Motion ◽

Stochastic Calculus

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Fractional Brownian motion: stochastic calculus and applications

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 ◽

10.4171/022-3/74 ◽

2009 ◽

pp. 1541-1562 ◽

Cited By ~ 6

Author(s):

David Nualart

Keyword(s):

Brownian Motion ◽

Fractional Brownian Motion ◽

Stochastic Calculus

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