کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1156494 958834 2015 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nourdin–Peccati analysis on Wiener and Wiener–Poisson space for general distributions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Nourdin–Peccati analysis on Wiener and Wiener–Poisson space for general distributions
چکیده انگلیسی

Given a reference random variable, we study the solution of its Stein equation and obtain universal bounds on its first and second derivatives. We then extend the analysis of Nourdin and Peccati by bounding the Fortet–Mourier and Wasserstein distances from more general random variables such as members of the Exponential and Pearson families. Using these results, we obtain non-central limit theorems, generalizing the ideas applied to their analysis of convergence to Normal random variables. We do these in both Wiener space and the more general Wiener–Poisson space. In the former space, we study conditions for convergence under several particular cases and characterize when two random variables have the same distribution. In the latter space we give sufficient conditions for a sequence of multiple (Wiener–Poisson) integrals to converge to a Normal random variable.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 125, Issue 1, January 2015, Pages 182–216
نویسندگان
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