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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)Gene regulatory network inference from sparsely sampled noisy data Aalto, Atte ; ; et al in Nature Communications (2020), 11 The complexity of biological systems is encoded in gene regulatory networks. Unravelling this intricate web is a fundamental step in understanding the mechanisms of life and eventually developing ... [more ▼] The complexity of biological systems is encoded in gene regulatory networks. Unravelling this intricate web is a fundamental step in understanding the mechanisms of life and eventually developing efficient therapies to treat and cure diseases. The major obstacle in inferring gene regulatory networks is the lack of data. While time series data are nowadays widely available, they are typically noisy, with low sampling frequency and overall small number of samples. This paper develops a method called BINGO to specifically deal with these issues. Benchmarked with both real and simulated time-series data covering many different gene regulatory networks, BINGO clearly and consistently outperforms state-of-the-art methods. The novelty of BINGO lies in a nonparametric approach featuring statistical sampling of continuous gene expression profiles. BINGO’s superior performance and ease of use, even by non-specialists, make gene regulatory network inference available to any researcher, helping to decipher the complex mechanisms of life. [less ▲] Detailed reference viewed: 224 (25 UL)Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model Azmoodeh, Ehsan ; ; in Modern Stochastics: Theory and Applications (2015), 2(1), 2949 Detailed reference viewed: 96 (6 UL)Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind Azmoodeh, Ehsan ; in Statistical Inference for Stochastic Processes (2015), 18(3), 205227 Detailed reference viewed: 111 (1 UL)Necessary and sufficient conditions for Hölder continuity of Gaussian processes Azmoodeh, Ehsan ; ; et al in Statistics and Probability Letters (2014), 94 The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note ... [more ▼] The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition. [less ▲] Detailed reference viewed: 100 (1 UL)Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model Azmoodeh, Ehsan ; ; E-print/Working paper (2014) We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst ... [more ▼] We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter H of the fractional part satisfies H∈(3/4,1), the central limit theorem holds. In the nonsemimartingale case, that is, where H∈(1/2,3/4], the convergence toward the normal distribution with a nonzero mean still holds if H=3/4, whereas for the other values, that is, H∈(1/2,3/4), the central convergence does not take place. We also provide Berry--Esseen estimates for the estimator. [less ▲] Detailed reference viewed: 103 (0 UL)A general approach to small deviation via concentration of measures Azmoodeh, Ehsan ; E-print/Working paper (2014) Detailed reference viewed: 52 (0 UL)Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion Azmoodeh, Ehsan ; in Journal of Theoretical Probability (2013) In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a ... [more ▼] In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a large class of convex functions $f$ is considered. In $\big[$\cite{a-m-v}, Statistics \& Decisions, \textbf{27}, 129-143$\big]$, for any convex function $f$, the almost sure convergence of uniform discretization to such stochastic integral is proved. Here we prove $L^r$- convergence of uniform discretization to stochastic integral. In addition, we obtain a rate of convergence. It turns out that the rate of convergence can be brought arbitrary close to $H - \frac{1}{2}$. [less ▲] Detailed reference viewed: 144 (4 UL)Parameter estimation based on discrete observations of fractional Ornstein-Uhlenbeck process of the second kind Azmoodeh, Ehsan ; E-print/Working paper (2013) Detailed reference viewed: 89 (1 UL) |
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