Minimizing the time spent in an interval by a Wiener process with uniform jumps

• Autorzy: Lefebvre Mario
• Języki publikacji: EN

Abstrakty

EN

Let X_u(t) be a controlled Wiener process with jumps that are uniformly distributed over the interval [−c, c]. The aim is to minimize the time spent by X_u(t) in the interval [a, b]. The integro- differential equation, satisfied by the value function, is transformed into an ordinary differential equation and is solved explicitly for a particular case. The approximate solution obtained is precise when c is small.

Słowa kluczowe

EN

Brownian motion; Poisson process; first-passage time; optimal stochastic control; integro-differential equation

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2019
• Tom: Vol. 48, No. 3
• Strony: 407--415
• Opis fizyczny: Bibliogr. 5 poz., rys.

Twórcy

autor

Lefebvre Mario

• Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, Montréal, Québec, Canada H3C 3A7

Bibliografia

• Abundo, M. (2000) On first-passage times for one-dimensional jump-diffusion processes. Probability and Mathematical Statistics, 20, 2, 399-423.
• Kou, S.G. and Wang, H. (2003) First passage times of a jump diffusion process. Advances in Applied Probability, 35, 504-531.
• Lefebvre, M. (2014) LQG homing for jump-diffusion processes. ROMAI Journal, 10, 2, 1-6.
• Theodorou, E.A. and Todorov, E. (2012) Stochastic optimal control for nonlinear Markov jump diffusion processes. In: Proceedings of the American Control Conference, 1633-1639. DOI: 10.1109/ACC.2012.6315408
• Whittle, P. (1982) Optimization over Time, Vol. I. Wiley, Chichester.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).