It is a learn file approximately my paintings on sequential statistic~ in the course of 1980 - 1984. issues are handled that are heavily concerning one another and to the legislation of the iterated logarithm:· I) curved boundary first passage distributions of Brownian movement, eleven) optimum houses of sequential assessments with parabolic and approximately parabolic barriers. within the first bankruptcy I speak about the tangent approximation for Brownianmotion as an international approximation gadget. this can be an extension of Strassen' s method of t'he legislation of the iterated logarithm which connects result of fluctuation thought of Brownian movement with classical equipment of sequential records. within the moment bankruptcy I utilize those connections and derive optimum homes of exams of strength one and repeated importance checks for the simpiest version of sequential facts, the Brownian movement with unknown go with the flow. To either topics:there under1ies an asymptotic procedure that's heavily associated with huge deviation concept: the preventing obstacles recede to infinity. it is a famous procedure in sequential stötistics that is generally mentioned in Siegmund's contemporary booklet ·Sequential Analysis". This strategy additionally ends up in a few new insights in regards to the legislations of the iterated logarithm (LIL). even though the LIL has been studied for almost seventy years the idea remains to be universal that it applies just for huge sampIe sizes that may by no means be obser ved in perform.
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