Consider the class C of real-valued stochastic processes of the form Xt=m+mt+ξt, with discrete t=1,2,⋯, such that mt→0 and the ξt are random variables with normal distributions N(0,σt), where σt→0. Required is a sequence of estimators m^t for the parameter m, determined by X1,⋯,Xt and a stopping rule τ, such that for every ε>0 and 0
The author presents a review of solutions to the problem of constructing a fixed precision estimate of the mean in the Gaussian case. The conclusion is that no satisfactory solution exists. No new results are given.
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Existence, uniqueness and ergodicity of weak solutions to the equation of stochastic quantization in finite volume is obtained as a simple consequence of the Girsanov theorem.