| Issue |
ITM Web Conf.
Volume 34, 2020
International Conference on Applied Mathematics and Numerical Methods – third edition (ICAMNM 2020)
|
|
|---|---|---|
| Article Number | 01003 | |
| Number of page(s) | 8 | |
| Section | Plenary Lectures | |
| DOI | https://doi.org/10.1051/itmconf/20203401003 | |
| Published online | 03 December 2020 | |
Analytical solution to an LQG homing problem in two dimensions
Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succ. Centre-ville, Montréal, Québec H3C3A7, Canada
* e-mail: mlefebvre@polymtl.ca
An analytical solution is found to the problem of maximising the time spent in the first quadrant by the two-dimensional diffusion process (X(t), Y(t)), where Y(t) is a controlled Brownian motion and X(t) is proportional to its integral. Moreover, we force the process to exit the first quadrant through the y-axis. This type of problem is known as LQG homing and is very difficult to solve explicitly, especially in two or more dimensions. Here the partial differential equation satisfied by a transformation of the value function is solved by making use of the method of separation of variables. The exact solution is expressed as an infinite sum of Airy functions.
Key words: first-exit time / Brownian motion / partial differential equations / method of separation of variables
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.