Convergence of Stochastic Processes (Springer Series in Statistics)
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Contents:
Collet, A. Lambert, S. Karlin and J. Mcgregor , The differential equations of birth-and-death processes, and the Stieltjes moment problem , Transactions of the American Mathematical Society , vol. Karlin and H. Taylor , A first course in stochastic processes , Klesov , Rate of convergence of series of random variables , Ukrainian Mathematical Journal , vol. Kot , Elements of mathematical ecology , Limic and A.
Part 1 of the book, Stochastic Convergence, gives an exposition of such a theory following the ideas of J. A second goal is to use the weak convergence theory background devel oped in Part 1 to present an account of major components of the modern theory of empirical processes indexed by classes of sets and functions. The weak convergence theory developed in Part 1 is important for this, simply because the empirical processes studied in Part 2, Empirical Processes, are naturally viewed as taking values in nonseparable Banach spaces, even in the most elementary cases, and are typically not Borel measurable.
Much of the theory presented in Part 2 has previously been scattered in the journal literature and has, as a result, been accessible only to a relatively small number of specialists. In view of the importance of this theory for statis tics, we hope that the presentation given here will make this theory more accessible to statisticians as well as to probabilists interested in statistical applications.
Weak Convergence and Empirical Processes
Thaele : A new quantitative central limit theorem on the Wiener space with applications to Gaussian processes A. Grygierek and C. Neufcourt and F. Sottinen and L. Bachmann and G. Bai and M. Bai, M. Ginovyan and M. Bally and L. Gaussian limits E.
Peccati and G. Jacob, M. Takeda and T.
Reitzner : U-statistics in stochastic geometry , book chapter J. Main article: Convergence of random variables. Nourdin : Exact rate of convergence of some approximation schemes associated to SDEs driven by a fBm. Reinert : Stein's method and stochastic analysis of Rademacher sequences , Elect. The TwoSample Problem.
Uemura, eds. El Onsy, K. Thaele : A four moments theorem for Gamma limits on a Poisson chaos D. Harnett and D.
Where we are
Nualart : Central limit theorem for functionals of a generalized self-similar process A. Nualart : Asymptotic properties of the derivative of self-intersection local time of fractional Brownian motion Y. Krokowski, A. Reichenbachs and C. Thaele : Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs, point processes and percolation S. Kusuoka and C. Tudor : Characterization of the convergence in total variation and extension of the Fourth Moment Theorem to invariant measures of diffusions R.
Reitzner : U-statistics in stochastic geometry , book chapter J. Liu, D. Tang and Y. Mourrat and J. Nolen : Scaling limit of the corrector in stochastic homogenization G. Naitzat and R. Adler : A central limit theorem for the Euler integral of a Gaussian random field L. Nicolaescu : Critical points of multidimensional random Fourier series: central limits L.
Nicolaescu : Wiener chaos and limit theorems I. Nualart and R. Zintout : Multivariate central limit theorems for averages of fractional Volterra processes and applications to parameter estimation I. Peccati, G. Poly and R. Simone : Multidimensional limit theorems for homogeneous sums: a general transfer principle D. Reitzner M. Schulte and C. Thaele : Poisson point process convergence and extreme values in stochastic geometry , Chapter of the forthcoming book Stochastic analysis for Poisson point processes: Malliavin calculus, Wiener-Ito chaos expansions and stochastic geometry edited by G.
Reitzner R. Simone : Universality and Fourth Moment Theorem for homogeneous sums. Torrisi : Gaussian approximation of nonlinear Hawkes processes , Ann. Applied Probab. Torrisi : Poisson approximation of point processes with stochastic intensity, and application to nonlinear Hawkes processes , Ann. Arizmendi and A. Dalmao and J. Poly : The law of iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds E. Poly : Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach E.
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Azmoodeh, T. Benes and M. Zikmundova : Functionals of spatial point processes having a density with respect to the Poisson process , Kybernetika 50 , no. Bourguin, C. Durastanti, D. Marinucci and G. Peccati : Gaussian approximations of nonlinear statistics on the sphere Y. Eichelsbacher and C. Estrade and J. Leon : A central limit theorem for the Euler characteristic of a Gaussian excursion set L.
Goldstein, I. Hu, Y. Liu and D.
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Kim : Weak convergence for multiple stochastic integrals in Skorohod space , Korean J. Thaele : Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences N. Kuang and B.
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Springer Series in Statistics Convergence of Stochastic Processes Interesting Facts About Weak Convergence, and Applications to Mathematical Statistics. Pollard, D.:Convergence of stochastic processes. (Springer series in statistics). Springer‐Verlag, New York ‐ Berlin ‐ Heidelberg ‐ Tokyo , pp.
Peccati : Strong asymptotic independence on Wiener chaos I. Simone : Classical and free fourth moment theorems: universality and thresholds D. Olivera and C. Tudor : The density of the solution to the stochastic transport equation with fractional noise M. Pakkanen and A. Ruiz-Medina and R. Theory Probab. Thaele : Cumulants on Wiener chaos: moderate deviations and the fourth moment theorem R.