How is P{ Bt > a | Ta <= t } = 1/2 an appropriate description of the reflection principle of Brownian motion? Shouldn't the inequality in the denominator be "less than" instead of "less than or equal to"?
In the case where Ta = t exactly, I would think that Bt = a exactly; or, in other words, Bt > a is not possible. Please see the attached plot of Brownian motion from Probability and Random Processes (Ramon van Handel) that visualizes Bt and Ta: p158
