Existence of solutions and optimal control for reflecting stochastic differential equations with applications to population control theory*
作者:
Situ Rong,
W.L. Chan,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1992)
卷期:
Volume 10,
issue 1
页码: 45-106
ISSN:0736-2994
年代: 1992
DOI:10.1080/07362999208809256
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
For the d–dimensional reflecting stochastic differential equations (1) with non-smooth boundary and unbounded domain the existence of a strong solution, (weak solution) is obtained under the conditions that the coefficients are less than linear growth and they are non-Lipschitz, (and the diffusion coefficient is non-degenerate, the drift coefficient is bounded and measurable only). Moreover, the Girsanov theorem and the martingale representation theorem with respect to system (1) are also derived. Then by using the Ekeland lemma and the martingale method the existence, necessary and sufficient conditions for an optimal control and an optimal control are obtained. The results are then applied to solve an optimal control problem for a stochastic population model
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