![]() We show it is characterized by a second order integro-differential equation, that the unknown value function solves on the continuation region, and by the smooth fit principle, which holds at the unknown boundary points. The method of proof consists of reducing the original optimal stopping problem to a free-boundary problem. One of the most classical problems arising in statistical sequential analysis is the sequential hypothesis testing (see 21). Muliere P., Sequential Testing Problems for Levy Processes, Seq. The Wald sequential probability ratio test (SPRT) is known to be optimal in this context for a large class of observable processes (see 5, 6, 2). Several examples are presented.ĪB - We study the Bayesian problem of sequential testing of two simple hypotheses about the Lévy-Khintchine triplet of a Lévy process, having diffusion component, represented by a Brownian motion with drift, and jump component of finite variation. Problems in sequential decision between hypotheses for a combined Poisson process. The method of proof consists of reducing the original optimal stopping problem to a free-boundary problem. N2 - We study the Bayesian problem of sequential testing of two simple hypotheses about the Lévy-Khintchine triplet of a Lévy process, having diffusion component, represented by a Brownian motion with drift, and jump component of finite variation. H a, we sample individual observations one at a time, and assess in a series of separate steps whether or not the accumulated information favors departure from H 0: Step 0: Begin by setting two constants, A and B, such that 0 < A < 1 < B. ![]() As usual in this framework, the initial optimal stopping problem is reduced to a free-boundary problem, solved through the principles of the smooth and/or continuous fit. ![]() T1 - Bayesian sequential testing for Lévy processes with diffusion and jump components We present the sequential testing of two simple hypotheses for a large class of Lévy processes. ![]()
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