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The discrepancy between min-max statistics of Gaussian and Gaussian-subordinated matrices Peccati, Giovanni ; Turchi, Nicola in Stochastic Processes and Their Applications (2023), 158 Detailed reference viewed: 54 (1 UL)Local times and sample path properties of the Rosenblatt process Kerchev, George ; Nourdin, Ivan ; et al in Stochastic Processes and Their Applications (2021), 131 Detailed reference viewed: 88 (6 UL)The Breuer-Major Theorem in total variation: improved rates under minimal regularity Nourdin, Ivan ; ; Peccati, Giovanni in Stochastic Processes and Their Applications (2021), 131 Detailed reference viewed: 132 (9 UL)Stein’s method for multivariate Brownian approximations of sums under dependence Kasprzak, Mikolaj in Stochastic Processes and Their Applications (2020), 130(8), 4927-4967 Detailed reference viewed: 105 (15 UL)Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes Amorino, Chiara ; in Stochastic Processes and Their Applications (2020) The problem of integrated volatility estimation for an Ito semimartingale is considered under discrete high-frequency observations in short time horizon. We provide an asymptotic expansion for the ... [more ▼] The problem of integrated volatility estimation for an Ito semimartingale is considered under discrete high-frequency observations in short time horizon. We provide an asymptotic expansion for the integrated volatility that gives us, in detail, the contribution deriving from the jump part. The knowledge of such a contribution allows us to build an unbiased version of the truncated quadratic variation, in which the bias is visibly reduced. In earlier results to have the original truncated realized volatility well-performed the condition β> 1 /2 (2− α) on β (that is such that (1/ n)^β is the threshold of the truncated quadratic variation) and on the degree of jump activity α was needed (see Mancini, 2011; Jacod, 2008). In this paper we theoretically relax this condition and we show that our unbiased estimator achieves excellent numerical results for any couple (α, β). [less ▲] Detailed reference viewed: 37 (3 UL)Malliavin and Dirichlet structures for independent random variables Halconruy, Hélène ; in Stochastic Processes and Their Applications (2019), 129(8), 2611-2653 On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual ... [more ▼] On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron-Stein inequality can be interpreted as a Poincaré inequality or that the Hoeffding decomposition of U-statistics can be interpreted as an avatar of the Clark representation formula. Thanks to our framework, we obtain a bound for the distance between the distribution of any functional of independent variables and the Gaussian and Gamma distributions. [less ▲] Detailed reference viewed: 67 (11 UL)Statistical inference for Vasicek-type model driven by Hermite processes Nourdin, Ivan ; Tran, Thi Thanh Diu in Stochastic Processes and Their Applications (2019), 129(10), 3774-3791 Detailed reference viewed: 232 (11 UL)On sojourn of Brownian motion inside moving boundaries. ; Yang, Xiaochuan in Stochastic Processes and Their Applications (2019) Detailed reference viewed: 180 (0 UL)First Order Feynman-Kac Formula ; Thompson, James in Stochastic Processes and Their Applications (2018) We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and for their derivatives ... [more ▼] We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and for their derivatives, given in terms of a Gaussian term and the semi-classical bridge. Assumptions are on the Riemannian data. [less ▲] Detailed reference viewed: 216 (35 UL)Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals Zheng, Guangqu in Stochastic Processes and Their Applications (2017), 127(5), 1622-1636 In this work, we study the normal approximation and almost sure central limit theorems for some functionals of an independent sequence of Rademacher random variables. In particular, we provide a new chain ... [more ▼] In this work, we study the normal approximation and almost sure central limit theorems for some functionals of an independent sequence of Rademacher random variables. In particular, we provide a new chain rule that improves the one derived by Nourdin et al. (2010) and then we deduce the bound on Wasserstein distance for normal approximation using the (discrete) Malliavin–Stein approach. Besides, we are able to give the almost sure central limit theorem for a sequence of random variables inside a fixed Rademacher chaos using the Ibragimov–Lifshits criterion [less ▲] Detailed reference viewed: 130 (7 UL)Rho-estimators for shape restricted density estimation Baraud, Yannick ; in Stochastic Processes and Their Applications (2016), 126(12), 3888--3912 Detailed reference viewed: 133 (25 UL)A probabilistic method for gradient estimates of some geometric flows ; Cheng, Li Juan ; in Stochastic Processes and Their Applications (2015), 125(6), 2295--2315 Detailed reference viewed: 201 (29 UL)A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric Guo, Hongxin ; Philipowski, Robert ; Thalmaier, Anton in Stochastic Processes and Their Applications (2014), 124(11), 3535-3552 We first prove stochastic representation formulae for space–time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems ... [more ▼] We first prove stochastic representation formulae for space–time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems under appropriate curvature conditions. Space–time harmonic mappings which are defined globally in time correspond to ancient solutions to the harmonic map heat flow. As corollaries, we establish triviality of such ancient solutions in a variety of different situations. [less ▲] Detailed reference viewed: 302 (30 UL)Representation of Gaussian isotropic spin random fields ; Rossi, Maurizia in Stochastic Processes and Their Applications (2014) Detailed reference viewed: 101 (1 UL)Comparison inequalities on the Wiener space Nourdin, Ivan ; Peccati, Giovanni ; in Stochastic Processes and Their Applications (2014), 124(4), 1566-1581 Detailed reference viewed: 136 (3 UL)Fine Gaussian fluctuations on the Poisson space II: Rescaled kernels, marked processes and geometric $U$-statistics ; Peccati, Giovanni in Stochastic Processes and Their Applications (2013), 123(12), 4186--4218 Detailed reference viewed: 162 (3 UL)Convergence in total variation on Wiener chaos Nourdin, Ivan ; in Stochastic Processes and Their Applications (2013), 123 Detailed reference viewed: 112 (3 UL)An invariance principle under the total variation distance Poly, Guillaume Joseph ; Nourdin, Ivan in Stochastic Processes and Their Applications (2013) Detailed reference viewed: 183 (2 UL)Quantitative Breuer-Major theorems Nourdin, Ivan ; Peccati, Giovanni ; in Stochastic Processes and Their Applications (2011), 121(4), 793--812 Detailed reference viewed: 200 (3 UL)Weak approximation of a fractional SDE ; Nourdin, Ivan ; et al in Stochastic Processes and Their Applications (2010), 120 Detailed reference viewed: 129 (4 UL) |
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