Let (X sim mathrm{N}(0,1)). Show that for every (lambda_{0} inleft(0, frac{1}{2}ight)) there is a constant (C=Cleft(lambda_{0}ight)) such
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Let \(X \sim \mathrm{N}(0,1)\). Show that for every \(\lambda_{0} \in\left(0, \frac{1}{2}ight)\) there is a constant \(C=C\left(\lambda_{0}ight)\) such that \(\sup _{\lambda \leqslant \lambda_{0}} \mathbb{E}\left(\left(X^{2}-1ight)^{2} e^{|\lambda|\left(X^{2}-1ight)}ight) \leqslant C<\infty\).
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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook
ISBN: 9783110741254
3rd Edition
Authors: René L. Schilling, Björn Böttcher
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