# Bayesian sequential testing of the drift of a Brownian motion

@article{Ekstrom2015BayesianST, title={Bayesian sequential testing of the drift of a Brownian motion}, author={Erik Ekstrom and Juozas Vaicenavicius}, journal={arXiv: Probability}, year={2015} }

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior distributions. The statistical problem is reformulated as an optimal stopping problem with the current conditional probability that the drift is non-negative as the underlying process. The volatility of this conditional probability process is shown to be non-increasing…

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## References

SHOWING 1-10 OF 21 REFERENCES

### SEQUENTIAL TEST FOR THE MEAN OF A NORMAL DISTRIBUTION III (SMALL t)

- Mathematics
- 1965

Abstract : Asymptotic expansions are derived for the behavior of the optimal sequential test of whether the unknown drift mu of a Wiener-Levy process is positive or negative for the case where the…

### Sequential Tests for the Mean of a Normal Distribution

- Mathematics
- 1961

Abstract : The problem of sequentially testing whether the mean of a normal distribution is positive has been approximated by the continous analogue where one must decide whether the mean drift of a…

### On Chernoff's Hypotheses Testing Problem for the Drift of a Brownian Motion

- Mathematics
- 2013

This paper contains detailed exposition of the results presented in the short communication [M. V. Zhitlukhin and A. A. Muravlev, Russian Math. Surveys, 66 (2011), pp. 1012--1013]. We consider…

### The Wiener Sequential Testing Problem with Finite Horizon

- Mathematics
- 2004

We present a solution of the Bayesian problem of sequential testing of two simple hypotheses about the mean value of an observed Wiener process on the time interval with finite horizon. The method of…

### On the Wiener process approximation to Bayesian sequential testing problems

- Mathematics
- 1972

This paper is concerned with the problem of testing H: 0 .

### Volatility time and properties of option prices

- Mathematics, Economics
- 2003

We use a notion of stochastic time, here called volatility time, to show convexity of option prices in the underlying asset if the contract function is convex as well as continuity and monotonicity…

### ON OPTIMAL STOPPING PROBLEMS IN SEQUENTIAL HYPOTHESIS TESTING

- Mathematics
- 1997

After a brief survey of a variety of optimal stopping problems in sequential testing theory, we give a unified treatment of these problems by introducing a gen- eral class of loss functions and prior…

### Optimal Stopping and the American Put

- Mathematics
- 1991

We show that the problem of pricing the American put is equivalent to solving an optimal stopping problem. the optimal stopping problem gives rise to a parabolic free-boundary problem. We show there…

### Probability theory - a comprehensive course

- MathematicsUniversitext
- 2008

Convergence Theorems are applied to the interpretation of Brownian Motion and the law of the Iterated Logarithm as well as to Martingales and Exchangeability.