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A large deviation principle in H\"older norm for multiple fractional integrals
Probability · Submitted 2 Feb 2007
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Then, it is proved that the family of probability laws of the processes obtained by replacing $B^H$ by $\epsilon^{{1/2}} B^H$ satisfies a large deviation principle in H\"older norm.
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The abstract, sentence by sentence
For a fractional Brownian motion $B^H$ with Hurst parameter $H\in]{1/4},{1/2}[\cup]{1/2},1[$, multiple indefinite integrals on a simplex are constructed and the regularity of their sample paths are studied. Then, it is proved that the family of probability laws of the processes obtained by replacing $B^H$ by $\epsilon^{{1/2}} B^H$ satisfies a large deviation principle in H\"older norm. The definition of the multiple integrals relies upon a representation of the fractional Brownian motion in terms of a stochastic integral with respect to a standard Brownian motion. For the large deviation principle, the abstract general setting given by Ledoux in [Lecture Notes in Math., vol. 1426 (1990) 1-14] is used.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | For a fractional Brownian motion $B^H$ with Hurst parameter $H\in]{1/4},{1/2}[\cup]{1/2},1[$, multiple indefinite integrals on a simplex are constructed and the regularity of their sample paths are studied. | contribution 1.00 | 0.91 | 0.08 | asserted 0.99 |
| s1 | Then, it is proved that the family of probability laws of the processes obtained by replacing $B^H$ by $\epsilon^{{1/2}} B^H$ satisfies a large deviation principle in H\"older norm. | result 0.97 | 0.94 | 0.84 | asserted 1.00 |
| s2 | The definition of the multiple integrals relies upon a representation of the fractional Brownian motion in terms of a stochastic integral with respect to a standard Brownian motion. | method 0.99 | 0.45 | 0.02 | asserted 1.00 |
| s3 | For the large deviation principle, the abstract general setting given by Ledoux in [Lecture Notes in Math., vol. 1426 (1990) 1-14] is used. | method 0.99 | 0.26 | 0.03 | asserted 1.00 |
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Original abstract
For a fractional Brownian motion $B^H$ with Hurst parameter $H\in]{1/4},{1/2}[\cup]{1/2},1[$, multiple indefinite integrals on a simplex are constructed and the regularity of their sample paths are studied. Then, it is proved that the family of probability laws of the processes obtained by replacing $B^H$ by $\epsilon^{{1/2}} B^H$ satisfies a large deviation principle in H\"older norm. The definition of the multiple integrals relies upon a representation of the fractional Brownian motion in terms of a stochastic integral with respect to a standard Brownian motion. For the large deviation principle, the abstract general setting given by Ledoux in [Lecture Notes in Math., vol. 1426 (1990) 1-14] is used.
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