Normal Approximations with Malliavin Calculus
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ISBN-13:
9781107017771
Veröffentl:
2015
Einband:
HC gerader Rücken kaschiert
Erscheinungsdatum:
14.04.2015
Seiten:
254
Autor:
Ivan Nourdin
Gewicht:
570 g
Format:
235x157x20 mm
Sprache:
Englisch
Beschreibung:
This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.
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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