Sequential probability ratio tests are defined for testing a simple hypothesis against a simple alternative for the mean value function of a real Gaussian process with known covariance kernel. Exact formulas are obtained for the error probabilities and the OC function using the fact that the $\log$ likelihood ratio process is a Gaussian process with independent increments and have continuous sample paths. An identity of a familiar nature holds for the expected value of the $\log$ likelihood ratio process at a random stopping time. In certain situations this identity yields an exact formula for the ASN function. Two examples are given. The analysis employs the theory of reproducing kernel Hilbert spaces.
"Sequential Probability Ratio Test for the Mean Value Function of a Gaussian Process." Ann. Math. Statist. 43 (6) 1861 - 1873, December, 1972. https://doi.org/10.1214/aoms/1177690857