ABSTRACT This work is concerne d with the application of the theor y of stochastic p r o c e s s e s , of potential theor y and of convex analysi s to the optimal control of diffusions. Ver y genera l result s of existenc e a r e prove d for diffusions killed on a Bore l set, for "dying" diffusions, for unidimensional homogeneous diffusions, and for diffusions reflected on a boundary. The result s a r e ver y general , and include all the alread y known t h e o r e m s on stochastic control , while extending them on numerou s points . AMS (MOS) subject classifications (1970). P r i m a r y 93E20, 60J60, 60J45, 49A30, 49B35 secondar y 60H05, 60G45. K e y w o r d s and p h r a s e s . Stochastic control theory, diffusions, probabilisti c potential theory , m a r t i n g a l e s . Library of Congress Cataloging in Publication Data W ^ | | J Bismut, Jea n Michel. Theori e p r o b a b i l i s t e du c o n t r M e des d i f f u s i o n s . (Memoirs of t h e American Mathematical Societ y no. 167) Summary i n E n g l i s h . Bibliography : p . 1. Diffusio n p r o c e s s e s . 2. Contro l t h e o r y . 3 . P o t e n t i a l , Theory of. k. Martinqale s (Math- ematics ) I . T i t l e . I I . S e r i e s : American Math- e m a t i c a l S o c i e t y . Memoirs no. 167. QA3.A57 no.167 [QA27lf.75] 510 T .8s [519.2*5] ISBN 0-8218-1867-8 75-J+l602 ii
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