Abstract
Consider the motion of a Brownian particle that takes place either in a two-dimensional plane or in three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the true dimension as soon as possible and with minimal probabilities of the wrong terminal decisions. We solve this problem in the Bayesian formulation under any prior probability of the true dimension when the passage of time is penalised linearly.
| Original language | English |
|---|---|
| Pages (from-to) | 2085-2113 |
| Number of pages | 29 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 370 |
| Issue number | 3 |
| Early online date | 8 Sept 2017 |
| DOIs | |
| Publication status | Published - 1 Jan 2018 |
Keywords
- Bessel process
- Brownian motion
- Entrance boundary
- Free-boundary problem
- Nonlinear Volterra integral equation
- Optimal stopping
- Parabolic partial differential equation
- Sequential testing
- Signal-to-noise ratio
- Smooth fit
- The change-of-variable formula with local time on curves