On certain discounted arc-sine laws

The Dynkin-lamperti Arc-sine Laws for Measure Preserving Transformations

Arc-sine laws in the sense of renewal theory are proved for return time processes generated by transformations with infinite invariant measure on sets satisfying a type of Darling-Kac condition, and an application to real transformations with indifferent fixed points is discussed.

Toward a Certain Equivalent Discounted Cash Flow Model

The Uniform Mixture of Generalized Arc-sine Distributions

A single, tractable, special case of the problem of continuous mixtures of beta distributions over their parameters is considered. This is the uniform mixture of generalized arc-sine distributions which, curiously, turns out to be linked by transformation to the Cauchy distribution. AMS 2000 subject classification. 62E15.

New Inequalities of Shafer-Fink Type for Arc Hyperbolic Sine

Asymptotic sine laws arising from alternating random permutations and sequences

In the last century, Desire Andre obtained many remarkable properties of the numbers of alternating permutations, linking them to trigonometric functions among other things. By considering the probability that a random permutation is alternating and that a random sequence (from a uniform distribution) is alternating, and by conditioning on the first element of the sequence, his results are exte...