References of "Stochastic Processes and Their Applications"
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See detailLocal times and sample path properties of the Rosenblatt process
Kerchev, George UL; Nourdin, Ivan UL; Saksman, Eero et al

in Stochastic Processes and Their Applications (2021), 131

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See detailThe Breuer-Major Theorem in total variation: improved rates under minimal regularity
Nourdin, Ivan UL; Nualart, David; Peccati, Giovanni UL

in Stochastic Processes and Their Applications (2021), 131

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See detailStein’s method for multivariate Brownian approximations of sums under dependence
Kasprzak, Mikolaj UL

in Stochastic Processes and Their Applications (2020), 130(8), 4927-4967

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See detailUnbiased truncated quadratic variation for volatility estimation in jump diffusion processes
Amorino, Chiara UL; Gloter, Arnaud

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 ▲]

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See detailMalliavin and Dirichlet structures for independent random variables
Halconruy, Hélène UL; Decreusefond, Laurent

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 ▲]

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See detailStatistical inference for Vasicek-type model driven by Hermite processes
Nourdin, Ivan UL; Tran, Thi Thanh Diu UL

in Stochastic Processes and Their Applications (2019), 129(10), 3774-3791

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See detailOn sojourn of Brownian motion inside moving boundaries.
Seuret, Stephane; Yang, Xiaochuan UL

in Stochastic Processes and Their Applications (2019)

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See detailA stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric
Guo, Hongxin UL; Philipowski, Robert UL; Thalmaier, Anton UL

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 ▲]

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