The conditional expectation and conditional variance of Brownian motion is considered given the argmax, B(t|argmax), as well as those with additional information: B(t|close, argmax), B(t|max, argmax), B(t|close, max, argmax) where the close is the final value: B(t=1)=c and t in [0,1]. We compute the expectation and variance of a Brownian meander in time. By splicing together two Brownian meanders, the mean and variance of the constrained process are calculated. Computational results displaying both the expectation and variance in time are presented. Comparison of the simulation with theoretical values are shown when the close and argmax are given.
翻译：B(t ⁇ clos, armax),B(t ⁇ clos, armax),B(t ⁇ clos, armax),B(t ⁇ max, armax),B(t ⁇ clos, 最大),B(t ⁇ c, armax)是最后值的接近值:B(t=1)=c和t ([0,1]),B(t ⁇ argmax),以及附加信息(B(t ⁇ clos, armax),以及B(t ⁇ c, argmax), 有条件的预期值和有条件差异,B(agmax, armax)和有条件的预期值,B(t ⁇ c, 最大),B(t)是最终值的接近值,B(t=1),B(t)和[0,1]。我们计算了一个棕色色蜂的预期值的预期值和差异。通过将两个Brown meands,计算出受限制过程的平均值和差异的平均值和平均值。提供了时间的比较结果的对比结果显示预期与模拟与理论的比较。
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