An analytical description of the time-integrated Brownian bridge

摘要: In animal movement research, the probability density function (PDF) of time-integrated Brownian bridge (TIBB) is used to delineate important regions on basis tracking data. Here, it assumed that an performs a between data points. As such, location at any moment in time individual performing described by normal distribution. The (time-independent) marginal given point, i.e., value PDF TIBB obtained averaging these distributions over time. To best our knowledge, thus far always computed through use numerical integration methods. we demonstrate nevertheless possible derive its analytical expression. Although two-dimensional setting most interesting one for studies, also one- and, general, n-dimensional are considered.