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1.
Jean-François Le Gall 《Probability Theory and Related Fields》1987,76(4):587-627
Summary LetW=(W
t, t0) denote a two-dimensional Brownian motion starting at 0 and, for 0<<, letC
be a wedge in 2 with vertex 0 and angle 2. We consider the set of timest's such that the path ofW, up to timet, stays inside the translated wedgeW
t-C. It follows from recent results of Burdzy and Shimura that this set, which we denote byH
, contains nonzero times if, and only if, >/4. Here we construct a measure, a local time, supported onH
. For /42, the Brownian motionW, time-changed by the inverse of this local time, is shown to be a two-dimensional stable process with index 2-/2. This results extends Spitzer's construction of the Cauchy process, which is recovered by taking =/2. A formula which describes the behaviour ofW before a timetH
is established and applied to the proof of a conjecture of Burdzy. We also obtain a two-dimensional version of the famous theorem of Lévy concerning the maximum process of linear Brownian motion. Precisely, for 0<2, letS
t denote the vertex of the smallest wedge of the typez-C
which contains the path ofW up to timet. The processS
t-Wt is shown to be a reflected Brownian motion in the wedgeC
, with oblique reflection on the sides. Finally, we investigate various extensions of the previous results to Brownian motion inR
d, d3. LetC
be the cone associated with an open subset of the sphereS
d-1, and letH
be defined asH
above. Sufficient conditions are given forH
to contain nonzero times, in terms of the first eigenvalue of the Dirichlet Laplacian on . 相似文献
2.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(10):1133-1136
We prove that the renormalized intersection local time of the planar Brownian motion can be approximated almost surely by a discrete equivalent built with random walks. 相似文献
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Yves Benoist 《Inventiones Mathematicae》2000,141(1):149-193
One studies the subgroups of GL(m,ℝ) which preserve a properly convex cone of ℝ
m
and whose action on ℝ
m
is irreducible. In particular, one describes the Zariski closure of these subgroups. As an application, one describes the
Zariski closure G of the subgroups of GL(m,ℝ) all of whose elements have nothing but positive eigenvalues. For instance, one can get the group G=GL(m,ℝ) if and only if m≠≡2 modulo4.
Oblatum 22-I-1999 & 10-XI-1999?Published online: 21 February 2000 相似文献
Automorphismes des c?nes convexes
Résumé. On étudie les sous-groupes de GL(m,ℝ) qui préservent un c?ne convexe saillant de ℝ m et dont l’action sur ℝ m est irréductible. En particulier, on décrit les adhérences de Zariski possibles pour ces sous-groupes. Comme application, on décrit les adhérences de Zariski G possibles pour les sous-groupes de GL(m,ℝ) dont tous les éléments ont toutes leurs valeurs propres positives. Par exemple, le groupe G=GL(m,ℝ) convient si et seulement si m≠≡2 modulo4.
Oblatum 22-I-1999 & 10-XI-1999?Published online: 21 February 2000 相似文献
5.
Sébastien Jansou 《Mathematische Annalen》2007,338(3):627-667
Résumé Pour un groupe réductif connexe complexe G, on classifie les modules simples dont le c?ne des vecteurs primitifs admet une déformation G-invariante non triviale. On relie cette classification à celle (due à Akhiezer) des variétés projectives lisses dont les
orbites sous l’action d’un groupe algébrique affine connexe sont un diviseur et son complémentaire.
Notre principal outil est le schéma de Hilbert invariant d’Alexeev et Brion; on en détermine les premiers exemples.
On détermine aussi les déformations infinitésimales (non nécessairement G-invariantes) des c?nes des vecteurs primitifs; elles sont triviales pour presque tous les modules simples.
Ce travail a été partiellement soutenu par le réseau Liegrits MRTN-CT 2003-505078. 相似文献
Ce travail a été partiellement soutenu par le réseau Liegrits MRTN-CT 2003-505078. 相似文献
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《Journal of Functional Analysis》1987,71(2):246-262
A precise meaning is given to the following intuitive statement: between the two times when it hits a double point, a Brownian motion behaves like a Brownian bridge. The main tool is the notion of intersection local time, which provides a measure on the set of double points, and hence a notion of properties of almost all double points. Results are applied to study points of infinite multiplicity of plane Brownian paths. 相似文献
8.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(5):559-564
Let (Bt)t≥0 be a standard Brownian motion starting at y, Xt = x+ ∫0tBs, ds, x ∈ (a, b). Let us set Tab = inf{t > 0 : Xt ∉ (a,b)}. In this paper, we compute the moments of the random variable BTa,b, and deduce the probability law of BTa,b. We show how to obtain the expectation E(x,y)(TabmBTabn). We also explicitly determine the probabilities P(x,y){XTab = a} and P(x,y) { XTab = b}. 相似文献
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W. Wolibner 《Mathematische Zeitschrift》1933,37(1):698-726
Sans résuméLes résultats de cette note ont été présentés au Deuxième Congrès des Mathematiciens polonais à Wilno le 26 Septembre 1931.Postérieurement à la rédaction de ce Mémoire j'ai appris que Monsieur J. Leray a indiqué le principe de la méthode que j'utilise, dans une Note publiée aux Compt. rend. de l'Academie des Sciences de Paris, le 30 mai 1932. 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(12):1385-1390
We derive a characterization of the dual cone of convex functions using second derivatives of positive symmetric matrices. This characterization allows us to determine the Euler-Lagrange equations associated to variational problems under convexity constraints. 相似文献
13.
J. Kampé de Fériet 《Annali di Matematica Pura ed Applicata》1962,60(1):29-36
Sans résumé
à M. Enrico Bompiani pour son Jubilé scientifique. 相似文献
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Jose Marie Orellana 《Comptes Rendus Mathematique》2010,348(21-22):1179-1183
Highly Active Anti-Retroviral Therapies (HAART) have proven to be extremely effective in improving and prolonging the patient's life. Though, a concern arises since a long term drug intake induces many strong sides effects and reduces reactivity of the virus to any therapy. The purpose of the paper is to use numerical analysis and optimization tools to suggest improved therapies to handle HIV infection. The evolution of the infection is modelled by an ordinary differential equation system which includes both immune response and multi-drug effects. For a fixed time, one looks for a two drugs control strategy based on Pontryagine's minimum principle with an objective function which takes into account three contributions: the viral load, the transient evolution of infection and the quantities of drug used. Simulations are carried out using an indirect optimization method along with Runge–Kutta adaptative stepsize algorithm. Numerical solutions to the optimality system are obtained and related histories are shown. The possibility of Scheduled Treatment Interruption is also examined. 相似文献
18.
Ivan Nourdin 《Comptes Rendus Mathematique》2005,340(8):611-614
We study here classical approximation schemes (Euler, Milshtein) associated with a differential equation of the type , , where g is a function, supposed Hölderian of order α somewhere in . When is the trajectory of fractional Brownian movement, we deduce probability properties to refine the results. To cite this article: I. Nourdin, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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