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Wiener process; Brownian bridge; symmetric process; sequential methods
In statistical inference on the drift parameter $a$ in the Wiener process with a constant drift $Y_{t} = at+W_{t}$ there is a large number of options how to do it. We may, for example, base this inference on the properties of the standard normal distribution applied to the differences between the observed values of the process at discrete times. Although such methods are very simple, it turns out that more appropriate is to use the sequential methods. For the hypotheses testing about the drift parameter it is more proper to standardize the observed process, and to use the sequential methods based on the first time when the process reaches either $B$ or $-B$, where $B>0$, until some given time. These methods can be generalized to other processes, for instance, to the Brownian bridges.
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