This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
Ivan Nourdin is Full Professor at Nancy University 1, France.
Inhaltsangabe
Preface Introduction 1. Malliavin operators in the one-dimensional case 2. Malliavin operators and isonormal Gaussian processes 3. Stein's method for one-dimensional normal approximations 4. Multidimensional Stein's method 5. Stein meets Malliavin: univariate normal approximations 6. Multivariate normal approximations 7. Exploring the Breuer¿Major Theorem 8. Computation of cumulants 9. Exact asymptotics and optimal rates 10. Density estimates 11. Homogeneous sums and universality Appendix 1. Gaussian elements, cumulants and Edgeworth expansions Appendix 2. Hilbert space notation Appendix 3. Distances between probability measures Appendix 4. Fractional Brownian motion Appendix 5. Some results from functional analysis References Index.
Preface Introduction 1. Malliavin operators in the one-dimensional case 2. Malliavin operators and isonormal Gaussian processes 3. Stein's method for one-dimensional normal approximations 4. Multidimensional Stein's method 5. Stein meets Malliavin: univariate normal approximations 6. Multivariate normal approximations 7. Exploring the Breuer¿Major Theorem 8. Computation of cumulants 9. Exact asymptotics and optimal rates 10. Density estimates 11. Homogeneous sums and universality Appendix 1. Gaussian elements, cumulants and Edgeworth expansions Appendix 2. Hilbert space notation Appendix 3. Distances between probability measures Appendix 4. Fractional Brownian motion Appendix 5. Some results from functional analysis References Index.
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