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Generalized Stein equation on extended class of functionsстатья
- Автор: Slepov N.A.
- Сборник: Proceedings of the International Conference Analytical and Computational Methods in Probability Theory and its Applications
- Глава в коллективной монографии
- Год издания: 2017
- Место издания: РУДН Москва
- Первая страница: 75
- Последняя страница: 79
- Аннотация: The aim of our work is to provide a generalization of the Stein equation allowing to use the functions f for which the classical Stein’s identity is not satisfied. We also show that our equation permits to characterize the law of X, i.e. this equation holds for all f in the extended F if and only if Law(Y) = P. In the operator theory framework one can observe that a so-called density approach is a particular case of our method. Due to the modification proposed we can estimate a distance between the target distribution P of a random variable X and a distribution of Y when supp(Y) is not a subset of supp(X). Moreover, we can write the characteristic Stein equations for random variables with non-interval support. We illustrate some advantages of the introduced method by a number of interesting examples.
- Добавил в систему: Слепов Николай Алексеевич