The proposed numerical technique is employed in well-understood problems to assess its efficiency. Hence, instead of solving the problem analytically, we use a collocation technique: the value function is replaced by a truncated series of polynomials with unknown coefficients that, together with the boundary points, are determined by forcing the series to satisfy the boundary conditions and, at fixed points, the integro-differential equation. ![]() Due to the form of the Lévy measure of a gamma process, determining the solution of this equation and the boundaries is not an easy task. In this paper, we present the testing of four hypotheses on two streams of observations that are driven by Lévy processes. Now it is time to test the models and to check if they fit the real data and what. ![]() The initial optimal stopping problem is reduced to a free-boundary problem where, at the unknown boundary points separating the stopping and continuation set, the principles of the smooth and/or continuous fit hold and the unknown value function satisfies on the continuation set a linear integro-differential equation. A Poisson process is a sequence of random variables with jump size 1. The Wald's sequential probability ratio test (SPRT) of two simple hypotheses regarding the Lvy-Khintchine triplet of a wide family of Lvy processes is analyzed: we concentrate on continuous paths and pure increasing jump Lvy processes. Sequential hypothesis testing concerns the speed-accuracy trade-off: deciding quickly versus reliably on a set of alternatives. We study the Bayesian problem of sequential testing of two simple hypotheses about the parameter α > 0 of a Lévy gamma process.
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