Showing papers by "Paris Dauphine University published in 1985"

Two remarks on Monge-Ampere equations

Abstract: We consider real Monge-Ampere equations and we present two new properties of these equations. First, we show the existence of the «first eigenvalue of Monge-Ampere equation» i.e. we show the existence of a positive constant possessing all the properties of the first eigenvalue of a 2-nd order elliptic operator (positivity, uniqueness of the eigenfunction, maximum principle, bifurcation...).The second property concerns variational characterisations of solutions. Both properties are closely related to similar properties of the general class of Hamilton-Jacobi-Bellman equations.

Regularizing effects for first-order hamilton-jacobi equations

Abstract: General regularizing effects for first-order Hamilton-Jacobi equations are proved. Applications to the Cauchy problem are also given.

An impulse control problem for a stochastic PDE arising in non linear filtering

Abstract: We c o n s i d e r t h e n o n l i n e a r f i l t e r i n g p r o b l e m o f a v e c t o r d i f f u s i o n p r o c e s s , when s e v e r a l n o i s y v e c t o r obs e r v a t i o n s w i t h p o s s i b l y d i f f e r e n t d i m e n s i o n o f t h e i r range space are a v a i l a b l e . A t each time any number of t h e s e o b s e r v a t i o n s ( o r s e n s o r s ) c a n b e u t i l i l i z e d i n t h e s i g n a l p r o c e s s i n g p e r f o r m e d by t h e n o n l i n e a r f i l t e r . The problem considered i s t h e o p t i m a l s e l e c t i o n o f a s c h e d u l e o f t h e s e s e n s o r s f r o m t h e a v a i l a b l e se t , so as t o o p t i m a l l y e s t i m a t e a f u n c t i o n o f t h e s t a t e a t t h e f i n a l t i m e . O p t i m a l i t y i s measured by a combined perform a n c e m e a s u r e t h a t a l l o c a t e s p e n a l t i e s f o r e r r o r s i n e s t i m a t i o n , s w i t c h i n g b e t w e e n s e n s o r s c h e d u l e s a n d f o r running a s e n s o r . The s o l u t i o n i s o b t a i n e d i n t h e f o r m of a s y s t e m o f q u a s i v a r i a t i o n a l i n e q u a l i t i e s i n t h e s p a c e o f s o l u t i o n s o f c e r t a i n Z a k a i e q u a t i o n s .

Labor and Investment Demand at the Firm Level: a Comparison of French, German and U.S. Manufacturing, 1970-79

Abstract: We investigate how labor and investment demand at the firm level (gross as well as net and replacement investment separately) differs in French, German and US manufacturing, and has changed since the 1974-75 crisis We use three consistent panel data samples of large firms for1970-79, and rely on simple models of the accelerator-profits type We find that the accelerator effects and the profits effects did not vary much between 1970-73 and 1976-79, and were quite comparable in the three countries, the former being of a more permanent nature and the latter more transitoryTo a large extent these effects account for the important changes and differences in labor and investment demand between the two subperiods and across the three countries