Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach


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No additional import charges at delivery! This item will be shipped through the Global Shipping Program and includes international tracking. Learn more - opens in a new window or tab. There are 2 items available. Add to basket. Stochastic Calculus and Applications Samuel N. Intersections of Random Walks Gregory F. Feynman-Kac Formulae Pierre del Moral.

Analysis of Variations for Self-similar Processes : A Stochastic Calculus Approach

Quasi-Stationary Distributions Pierre Collet. Stochastic Processes Andrei Borodin. Mass Transportation Problems Svetlozar T. Back cover copy Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades.

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In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrrelationship. Table of contents Preface. Fractional Brownian Motion and Related Processes. Non Gaussian Self-Similar Processes. Multiparameter Gaussian Processes. First and Second Order Quadratic Variations. Wavelet-Type Variations. Hermite Variations for Self-Similar Processes.

Kolmogorov Continuity Theorem. Multiple Wiener Integrals and Malliavin Derivatives. Review Text "The author provides the general theory for different classes of self-similar processes with a complete treatment of limit theorems for their variations. The book is self-contained and suitable for both graduate students with a basic background in probability theory and stochastic processes and researchers whose aim is investigating this topic.

It may serve as an excellent basis for research seminars or special classes on Gaussian processes and Malliavin's calculus and as a starting point for applied mathematicians with interest in self-similar processes. Woerner: Convergence of certain functionals of integral fractional processes. Journal of Theoretical Probability 23 , , Darses, I. Nourdin and D. Nualart: Limit theorems for nonlinear functionals of Volterra processes via white noise analysis. Bernoulli 16 4 , , Arxiv file. Nourdin, D. Tudor: Central and non-central limit theorems for weighted power variations of fractional Brownian Motion.

Annals de l'Institut Henri Poincare 46 , , Nualart: Central limit theorem for the third moment in space of the Brownian local time increments. Electronic Communications in Probability 15 , , Nualart: Central limit theorems for multiple Skorohod integrals. Nualart: Parameter estimation for fractional Ornstein-Uhlenbeck processes. Statistics and Probability Letters 80 , , Es-Sebaiy, D. Nualart, Y. Ouknine, C. Tudor: Occupation densities for certain processes related to fractional Brownian motion. Stochastics 82 , , Song: Feynman-Kac formula for heat equation driven by fractional white noise.

Annals of Probability 39 , , Nualart and L. Quer-Sardanyons: Optimal Gaussian density estimates for a class of stochastic equations with additive noise. Tindel: A construction of the rough path above fractional Brownian motion using Volterra's representation. Song: Malliavin calculus for backward stochastic differential equations and application to numerical solutions. Annals of Applied Probability. Stochastics and Dynamics 11 , , Ed: A. Tsoi, D. Nualart and G.

Yin, World Scientific , Nualart, X. Weilin and Z. Weiguo: Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observations. Acta Mathematica Scientia 31B , , Hu, F. Lu and D. Annals of Probability 40 , , Harnett and D. Nualart: Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes. Stochastic Processes and Their Applications. Nualart: Stochastic calculus for Gaussian processes and application to hitting times.

Communications in Stochastic Analysis 6 , , Stochastic Process and Their Applications , , Poly: Absolute continuity and convergence of densities for random vectors on Wiener chaos. Electronic Journal of Probability 18 , , Nualart: Central limit theorem for a Stratonovich integral with Malliavin Calculus.


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Annals of Probability 41 , , Nualart and F. Xu: Central limit theorem for an additive functional of the fractional Brownian motion II. Swanson: Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II. Xu: Central limit theorem for an additive functional of the fractional Brownian motion.

Nualart: Convergence of densities for some functionals of Gaussian processes. Journal of Theoretical Probability. Burdzy, D. Swanson: Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion. Probability Theory and Related Fields. Huang, Y. Stochastics 86 , , Xu: Central limit theorem for functionals of two independent fractional Brownian motions. Nualart and V. Xu: A second order limit law for occupation times of the Cauchy process. Podolskij: Asymptotics of weighted random sums. Communications in Applied and Industrial Mathematics 6 , no.


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  5. Deya, D. Annals of Probability 43 , , Hu, J. Huang, D. Electronic Journal in Probability 20 , , Tindel and F. Xu: Density convergence in the Breuer-Major theorem for Gaussian stationary sequences. Bernoulli 21 4 , , Essaky and D. Stochastic Processes and Their Applications 11 , , Journal of the Mathematical Society of Japan 67, no.

    Journal of Theoretical Probability 28 , , Peccati: Strong asymptotic independence on Wiener chaos. Proceedings of the AMS. Peccati: Quantitative stable limit theorems on the Wiener space. Annals of Probability 44 no 1, , Arxiv file. Hu, Y. Lui and D. Nualart: Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions. Annals of Applied Probability 26 no 2, , Huang and D.

    Analysis of Variations for Self-similar Processes : Ciprian A. Tudor :

    Nualart: On the intermittency front of stochastic heat equation driven by colored noises. Electronic Communications in Probabililty 21 no 21, , Liu and D. Nualart: Taylor schemes for rough differential equations and fractional diffusions. Zintout: Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation. Statistical Inference for Stochastic Processes 19 no 2, , Jaramillo and D.

    Nualart: Asymptotic properties of the derivative of self-intersection local itme of fractional Brownian motion.

    About this book

    Stochastic Processes and Their Applications , , Arxiv file. Tudor: The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals. Annals of Probability 45 , no 1, , Arxiv file. Huang, K. Le and D. Nualart: Large time asymptotics for the parabolic Anderson model driven by spatially correlated noise. Chen, Y. Tindel: Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise.

    Electronic Journal of Probability 22 , no. Nualart: Two-point correlation function and Feynman-Kac formula for the stochastic heat equation. Tindel: Young differential equations with power type nonlinearities. Le, D.

    Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach
    Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach
    Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach
    Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach
    Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach
    Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach Analysis of Variations for Self-similar Processes: A Stochastic Calculus Approach

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