Large deviations for multiple Wiener-Itô integral processes

Mayer-Wolf, Eddy; Nualart, David; Pérez‐Abreu, Víctor

doi:10.1007/bfb0084307

Cited by 14 publications

(17 citation statements)

References 12 publications

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“…[17], and can be represented as Poisson stochastic integrals with finite variance. Note that exact estimates for the tail probabilities of (quadratic) Wiener functionals have been obtained in [11], see also [5,13,18,19]. Here we present dimension free results for norms of vectors of independent quadratic functionals.…”

Section: Quadratic Wiener Functionalsmentioning

confidence: 94%

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Dimension Free and Infinite Variance Tail Estimates on Poisson Space

2007

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Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functionals, including Lévy's stochastic area and the square norm of Brownian paths. In the infinite variance case, various tail estimates such as stable ones are also presented.

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Section: Quadratic Wiener Functionalsmentioning

confidence: 94%

“…provided (J m (f t m )) t∈R+ is a process of m-th order integrals with a.s. continuous sample paths (see also Remark 4.3 in [18]). It is clear that for n = 1, m = 2 and p = +∞, (4.9) and (4.10) coincide.…”

Section: A = 2 Supmentioning

confidence: 97%

Dimension Free and Infinite Variance Tail Estimates on Poisson Space

2007

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“…Also, by using an extended contraction principle for large deviations (see Pérez-Abreu and Tudor [13] ) and the large deviations for multiple Wiener-Itô integrals (see Ledoux [8] and Mayer-Wolf et al [10] ), we deduce the large deviations for the one-dimensional distributions of fractional bilinear equations perturbed by a small noise.…”

Section: Introductionmentioning

confidence: 95%

Fractional Bilinear Stochastic Equations with the Drift in the First Fractional Chaos

Tudor

2004

Stochastic Analysis and Applications

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In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise. ORDER REPRINTS Tudor ORDER REPRINTSRemark 2.1. It is known that there exists a standard Brownian motion fW H t g t2T defined on the same probability space ðO; F; PÞ such that: (i) fB H t g t2T and fW H t g t2T generate the same filtration F. (ii) (Representation Formula). For each t 2 T;

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“…That is, we apply the LDP for Gaussian stochastic integrals depending on a parameter established in Ledoux (1990) and Mayer-Wolf et al (1992). The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%