Showing papers by "Paris Dauphine University published in 1986"
TL;DR: In this article, a simple method to approximate uniformly in Hilbert spaces uniformly continuous functions by C = 1,1 functions is presented, which relies on explicit inf-supconvolution formulas or equivalently on the solutions of Hamilton-Jacobi equations.
Abstract: We present here a simple method to approximate uniformly in Hilbert spaces uniformly continuous functions byC
1,1 functions. This method relies on explicit inf-sup-convolution formulas or equivalently on the solutions of Hamilton-Jacobi equations.
270 citations
TL;DR: In this article, the authors examined the extent to which outranking and MAUT decision-aid approaches differ on non-theoretical grounds and concluded that outranking outperforms MAUT.
97 citations
TL;DR: In this paper, implicit product theories are proposed to explain consumers' expectancies regarding the way product attributes are related. But the implicit product theory is not a complete understanding of how consumers draw inferences about uncertain product characteristics.
56 citations
TL;DR: In this paper, the authors considered a stochastic control problem where the coefficients aij and bi are smooth, periodic with respect to the second variable, and the matrix (aij)ij is uniformly elliptic.
Abstract: In this paper, we consider the following problem:
Here the coefficients aij and bi are smooth, periodic with respect to the second variable, and the matrix (aij)ij is uniformly elliptic. The Hamiltonian H is locally Lipschitz continuous with respect to uϵ and Duϵ, and has quadratic growth with respect to Duϵ. The Hamilton-Jacobi-Beliman equations of some stochastic control problems are of this type.
Our aim is to pass to the limit in (0ϵ) as ϵ tends to zero. We assume the coefficients bi to be centered with respect to the invariant measure of the problem (see the main assumption (3.13)). Then we derive L∞, H and W, p0 > 2, estimates for the solutions of (0ϵ). We also prove the following corrector's result:
This allows us to pass to the limit in (0ϵ) and to obtain
This problem is of the same type as the initial one. When (0ϵ) is the Hamilton-Jacobi-Bellman equation of a stochastic control problem, then (00) is also a Hamilton-Jacobi-Bellman equation but one corresponding to a modified set of controls.
28 citations
01 Jan 1986
5 citations
5 citations
01 Jan 1986
TL;DR: It has long been known that in the case of an ill-conditioned eigenproblem it is often advisable to group some eigenvalues and compute a basis in the corresponding invariant subspace.
Abstract: It has long been known that in the case of an ill-conditioned eigenproblem (close eigenvalues and/or almost parallel eigenvectors) it is often advisable to group some eigenvalues and compute a basis in the corresponding invariant subspace. Two defect correction methods based on this idea are studied and tested.
4 citations
01 Jan 1986
3 citations
01 Dec 1986
TL;DR: In particular, the relations between various control or differential games problems and the associated nonlinear partial differential equations can be completely justified as mentioned in this paper, and the relation between control and differential games can be justified.
Abstract: The dynamic programming argument leads to various partial differential equations in finite or in infinite dimensions. The lack of regularity of the value functions makes difficult in general the use of these equations. These difficulties may be solved by the notion of viscosity solutions introduced by M. G. Crandall and the author. In particular, the relations between various control or differential games problems and the associated nonlinear partial differential equations can be completely justified.
2 citations
01 Dec 1986
TL;DR: In this paper, an analytic approach to derive estimate for approximate filters in the case of high signal to noise ratio was presented, and the results were initially proven by J. PICARD [l] using probabilistic methods.
Abstract: INTRODUCTION We present an analytic approach to derive estimate for approximate filters in the case of high signal to noise ratio. The results were initially proven by J . PICARD [l] using probabilistic methods. The analytic technique is more elementary. We present the theory in the scalar case, but the method carries over to the vector case. 1 . SETTING OF THE PROBLEM 1 . l . Notation Assumptions We shall consider the following model
1 citations
01 Jan 1986