On the existence of optimal control for general stochastic equations
Abstract
In this paper we consider the problem of optimal control for general stochastic differential equation of Itô type. We prove the existence of solutions of this equation under weaker assumptions than in [2]. Moreover, we prove the compactness of the space of solutions and the existence of optimal control.
References
1. J. Błaż. Existence of weak solutions of ltô stochastic differential equations (to appear).
2. W.H. Fleming, M. Nisio, On the existence of optimal stochastic controls, J. Math. Mech. 15 (1966), 777-794.
3. I.I. Gihman, A.V. Skorohod, The theory of stochastic processes III, 1975 (in Russian).
4. K. Itô, M. Nisio, On stationary solutions of a stochastic differential equation, J. Math. Kyoto Univ. 4 (1964), 1-75.
5. R.S. Liptser, A.N. Shiryaev, Statistics of random processes, Warszawa, 1981 (Polish translation).
6. R. Rabczuk, Elementy nierówności różniczkowych, Warszawa, 1976.
2. W.H. Fleming, M. Nisio, On the existence of optimal stochastic controls, J. Math. Mech. 15 (1966), 777-794.
3. I.I. Gihman, A.V. Skorohod, The theory of stochastic processes III, 1975 (in Russian).
4. K. Itô, M. Nisio, On stationary solutions of a stochastic differential equation, J. Math. Kyoto Univ. 4 (1964), 1-75.
5. R.S. Liptser, A.N. Shiryaev, Statistics of random processes, Warszawa, 1981 (Polish translation).
6. R. Rabczuk, Elementy nierówności różniczkowych, Warszawa, 1976.
StolarczykM. (1990). On the existence of optimal control for general stochastic equations. Annales Mathematicae Silesianae, 3, 115-126. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14310
Maria Stolarczyk
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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