Hitting lines at minimal cost with a gaussian process

✍ Scribed by Mario Lefebvre

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 157 KB
• Volume: 26
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(90)90143-6

✦ Synopsis

Key Wo~ts--Stochastic control; stochastic systems; optimal control; random processes; partial differential equations; integral transforms.

Akstr~c~--Let dx(t)/dt = y(t) and dy(t)/dt = Bu(t) + e, where e is a Gaussian white noise such that y(t) is a process with lognormal transition density. Let S be the moment when the process y(t) hits a line in the upper half-plane for the first time. In this note, we obtain the control that minimizes the expected value of a cost function involving x(S).