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Original Articles

Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem

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Pages 1043-1056 | Published online: 30 Aug 2007

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (8)

Khalifa Es-Sebaiy. (2023) Gaussian and hermite Ornstein–Uhlenbeck processes. Stochastic Analysis and Applications 41:2, pages 394-423.
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Obayda Assaad, Charles-Phillipe Diez & Ciprian A. Tudor. (2023) Generalized Wiener–Hermite integrals and rough non-Gaussian Ornstein–Uhlenbeck process. Stochastics 95:2, pages 191-210.
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Rémi Dhoyer & Ciprian A. Tudor. (2022) Spatial average for the solution to the heat equation with Rosenblatt noise. Stochastic Analysis and Applications 40:6, pages 951-966.
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Qian Yu. (2020) Statistical inference for Vasicek-type model driven by self-similar Gaussian processes. Communications in Statistics - Theory and Methods 49:2, pages 471-484.
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V. M. Radchenko. (2019) Averaging principle for equation driven by a stochastic measure. Stochastics 91:6, pages 905-915.
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P. Čoupek. (2018) Limiting measure and stationarity of solutions to stochastic evolution equations with Volterra noise. Stochastic Analysis and Applications 36:3, pages 393-412.
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Litan Yan, Yumiao Li & Di Wu. (2017) Approximation of the Rosenblatt process by semimartingales. Communications in Statistics - Theory and Methods 46:9, pages 4556-4578.
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Ahmed Lahmoudi & El Hassan Lakhel. (2023) Fractional neutral functional differential equations driven by the Rosenblatt process with an infinite delay. Random Operators and Stochastic Equations 0:0.
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Ciprian A. Tudor. (2023) The overdamped generalized Langevin equation with Hermite noise. Fractional Calculus and Applied Analysis 26:3, pages 1082-1103.
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Atef Lechiheb. (2023) Wiener integrals with respect to the generalized Hermite process (gHp). Applications: SDEs with gHp noise. Random Operators and Stochastic Equations 31:1, pages 87-102.
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Héctor Araya, Johanna Garzón & Rolando Rubilar-Torrealba. (2023) Gamma mixed fractional Lévy Ornstein–Uhlenbeck process. Modern Stochastics: Theory and Applications, pages 1-21.
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Vadym Radchenko. (2023) The Burgers equation driven by a stochastic measure. Modern Stochastics: Theory and Applications, pages 229-246.
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Vadym Radchenko. (2023) Transport equation driven by a stochastic measure. Modern Stochastics: Theory and Applications, pages 197-209.
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Xuwen Cheng, Yiran Zheng & Xili Zhang. (2022) Arbitrage in the Hermite Binomial Market. Fractal and Fractional 6:12, pages 702.
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Petr Čoupek & Martin Ondreját. (2022) Besov-Orlicz Path Regularity of Non-Gaussian Processes. Potential Analysis.
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Martin Hairer & Xue-Mei Li. (2022) Generating Diffusions with Fractional Brownian Motion. Communications in Mathematical Physics 396:1, pages 91-141.
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Vadym M. Radchenko. 2022. General Stochastic Measures. General Stochastic Measures 231 239 .
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Johann Gehringer, Xue-Mei Li & Julian Sieber. (2022) Functional limit theorems for Volterra processes and applications to homogenization*. Nonlinearity 35:4, pages 1521-1557.
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Petr Čoupek, Bohdan Maslowski & Martin Ondreját. (2022) Stochastic integration with respect to fractional processes in Banach spaces. Journal of Functional Analysis 282:8, pages 109393.
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Johann Gehringer & Xue-Mei Li. (2020) Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process. Journal of Theoretical Probability 35:1, pages 426-456.
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A. Anguraj, K. Ramkumar, K. Ravikumar & Mamadou DiopAbdouAbdou. (2022) Exponential behavior of nonlinear stochastic partial functional equations driven by Poisson jumps and Rosenblatt process. Filomat 36:9, pages 2857-2870.
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R. Dhoyer & C. Tudor. (2022) Non-central limit theorem for the spatial average of the solution to the wave equation with Rosenblatt noise. Theory of Probability and Mathematical Statistics 106:0, pages 105-119.
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Johann Rudolf Gehringer. (2021) Functional limit theorems for power series with rapid decay of moving averages of Hermite processes. Stochastics and Dynamics 21:07.
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Valentin Garino, Ivan Nourdin, David Nualart & Majid Salamat. (2021) Limit theorems for integral functionals of Hermite-driven processes. Bernoulli 27:3.
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Guangjun Shen, Qian Yu & Zheng Tang. (2021) The Least Squares Estimator for an Ornstein-Uhlenbeck Process Driven by a Hermite Process with a Periodic Mean. Acta Mathematica Scientia 41:2, pages 517-534.
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Obayda Assaad & Ciprian A. Tudor. (2020) Parameter identification for the Hermite Ornstein–Uhlenbeck process. Statistical Inference for Stochastic Processes 23:2, pages 251-270.
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Radomyra Shevchenko & Ciprian A. Tudor. (2019) Parameter estimation for the Rosenblatt Ornstein–Uhlenbeck process with periodic mean. Statistical Inference for Stochastic Processes 23:1, pages 227-247.
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Ravikumar Kasinathan, Ramkumar Kasinathan, Mahamat Hassan Mahamat Hamit & Mamadou Abdoul Diop. (2020) Exponential behavior of neutral impulsive stochastic integro-differential equations driven by Poisson jumps and Rosenblatt process. Nonautonomous Dynamical Systems 7:1, pages 1-21.
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Meryem Slaoui & Ciprian A. Tudor. (2019) Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs. Journal of Mathematical Analysis and Applications 479:1, pages 350-383.
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Lakhel El Hassan. (2019) Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays. Proyecciones (Antofagasta) 38:4, pages 665-689.
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Ivan Nourdin & T.T. Diu Tran. (2019) Statistical inference for Vasicek-type model driven by Hermite processes. Stochastic Processes and their Applications 129:10, pages 3774-3791.
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Meryem Slaoui & C. A. Tudor. (2020) The linear stochastic heat equation with Hermite noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics 22:03, pages 1950022.
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STOYAN V. STOYANOV, SVETLOZAR T. RACHEV, STEFAN MITTNIK & FRANK J. FABOZZI. (2019) PRICING DERIVATIVES IN HERMITE MARKETS. International Journal of Theoretical and Applied Finance 22:06, pages 1950031.
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Zhe Chen, Lasse Leskelä & Lauri Viitasaari. (2019) Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes. Stochastic Processes and their Applications 129:8, pages 2723-2757.
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El Hassan Lakhel & M. A. McKibben. (2019) Controllability for Time-dependent Neutral Stochastic Functional Differential Equations with Rosenblatt Process and Impulses. International Journal of Control, Automation and Systems 17:2, pages 286-297.
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E. Lakhel & A. Tlidi. 2019. Recent Advances in Intuitionistic Fuzzy Logic Systems. Recent Advances in Intuitionistic Fuzzy Logic Systems 301 320 .
T. T. Diu Tran. (2018) Non-central limit theorems for quadratic functionals of Hermite-driven long memory moving average processes. Stochastics and Dynamics 18:04, pages 1850028.
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Pavel Chigansky & Marina Kleptsyna. (2018) Exact asymptotics in eigenproblems for fractional Brownian covariance operators. Stochastic Processes and their Applications 128:6, pages 2007-2059.
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Atef Lechiheb & Ezeddine Haouala. (2018) Fluctuations in 1D stochastic homogenization of pseudo-elliptic equations with long-range dependent potentials. Random Operators and Stochastic Equations 26:1, pages 23-37.
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Zhi Li, Litan Yan & Xianghui Zhou. (2017) Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process. Frontiers of Mathematics in China 13:1, pages 87-105.
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Vadym Radchenko & Nelia Stefans’ka. (2018) Approximation of solutions of the stochastic wave equation by using the Fourier series. Modern Stochastics: Theory and Applications, pages 429-444.
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Guangjun Shen & Qian Yu. (2017) An Optimal Approximation of Rosenblatt Sheet by Multiple Wiener Integrals. Mediterranean Journal of Mathematics 14:2.
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Denis Bell & David Nualart. (2017) Noncentral limit theorem for the generalized Hermite process. Electronic Communications in Probability 22:none.
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Ansgar Steland. (2015) Asymptotics for random functions moderated by dependent noise. Statistical Inference for Stochastic Processes 19:3, pages 363-387.
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Guangjun Shen, Xiuwei Yin & Litan Yan. (2015) Approximation of the Rosenblatt Sheet. Mediterranean Journal of Mathematics 13:4, pages 2215-2227.
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El Hassan Lakhel. (2016) Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps. Random Operators and Stochastic Equations 24:2, pages 113-127.
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Alexis Fauth & Ciprian A. Tudor. 2016. Handbook of High-Frequency Trading and Modeling in Finance. Handbook of High-Frequency Trading and Modeling in Finance 221 249 .
Guangjun Shen, Xiuwei Yin & Dongjin Zhu. (2015) Weak convergence to Rosenblatt sheet. Frontiers of Mathematics in China 10:4, pages 985-1004.
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Guangjun Shen & Yong Ren. (2015) Neutral stochastic partial differential equations with delay driven by Rosenblatt process in a Hilbert space. Journal of the Korean Statistical Society 44:1, pages 123-133.
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Litan Yan, Yumiao Li & Di Wu. (2015) Approximating the Rosenblatt process by multiple Wiener integrals. Electronic Communications in Probability 20:none.
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Christian Krein. (2015) Drift estimation with non-gaussian noise using Malliavin Calculus. Electronic Journal of Statistics 9:2.
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Jorge Clarke De la Cerda & Ciprian A. Tudor. (2014) Wiener integrals with respect to the Hermite random field and applications to the wave equation. Collectanea Mathematica 65:3, pages 341-356.
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Jan Beran, Arno Weiershäuser, C. Giovanni Galizia, Julia Rein, Brian H. Smith & Martin Strauch. (2013) On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data. Sankhya B 76:1, pages 49-81.
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Shuyang Bai & Murad S. Taqqu. (2014) Generalized Hermite processes, discrete chaos and limit theorems. Stochastic Processes and their Applications 124:4, pages 1710-1739.
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Ciprian A. Tudor. (2013) Recent developments on stochastic heat equation with additive fractional-colored noise. Fractional Calculus and Applied Analysis 17:1, pages 224-246.
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Soledad Torres, Ciprian Tudor & Frederi Viens. (2014) Quadratic variations for the fractional-colored stochastic heat equation. Electronic Journal of Probability 19:none.
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Xichao Sun & Ronglong Cheng. (2014) A Weak Convergence to Hermite Process by Martingale Differences. Advances in Mathematical Physics 2014, pages 1-10.
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Hanae Ouahhabi & Ciprian A. Tudor. (2013) Additive Functionals of the Solution to Fractional Stochastic Heat Equation. Journal of Fourier Analysis and Applications 19:4, pages 777-791.
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Ciprian TudorCiprian A. Tudor. 2013. Analysis of Variations for Self-similar Processes. Analysis of Variations for Self-similar Processes 77 101 .
Ciprian TudorCiprian A. Tudor. 2013. Analysis of Variations for Self-similar Processes. Analysis of Variations for Self-similar Processes 27 75 .
Chao Chen, Liya Sun & Litan Yan. (2012) An approximation to the Rosenblatt process using martingale differences. Statistics & Probability Letters 82:4, pages 748-757.
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S. Bonaccorsi & C. A. Tudor. (2011) Dissipative Stochastic Evolution Equations Driven by General Gaussian and Non-Gaussian Noise. Journal of Dynamics and Differential Equations 23:4, pages 791-816.
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Natallia Makarava, Sabah Benmehdi & Matthias Holschneider. (2011) Bayesian estimation of self-similarity exponent. Physical Review E 84:2.
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K. Es-Sebaiy & C. A. Tudor. (2011) Noncentral Limit Theorem for the Cubic Variation of a Class of Self-Similar Stochastic Processes. Theory of Probability & Its Applications 55:3, pages 411-431.
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Ngai Hang Chan & Wei Wei Liu. (2010) Residual empirical processes for nearly unstable long-memory time series. Journal of the Korean Statistical Society 39:3, pages 337-345.
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Andreas Basse-O’Connor & Svend-Erik Graversen. (2010) Path and semimartingale properties of chaos processes. Stochastic Processes and their Applications 120:4, pages 522-540.
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Khalifa Es-Sebaiy, Khalifa Es-Sebaiy, C A Tudor & C A Tudor. (2010) Noncentral limit theorem for the cubic variation of a class of self-similar stochastic processesNoncentral limit theorem for the cubic variation of a class of self-similar stochastic processes. Теория вероятностей и ее применения Teoriya Veroyatnostei i ee Primeneniya 55:3, pages 507-529.
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Alexandra Chronopoulou, Frederi G. Viens & Ciprian A. Tudor. (2009) Variations and Hurst index estimation for a Rosenblatt process using longer filters. Electronic Journal of Statistics 3:none.
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Ciprian A. Tudor. (2008) Analysis of the Rosenblatt process. ESAIM: Probability and Statistics 12, pages 230-257.
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