Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

On deformations of Hamiltonian actions

In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the symplectic form on the manifold. Received: 21 March 2006     

Parabolic equations of Von Karman type on Kähler manifolds

We study a parabolic version of a system of Von Karman type on a compact Kähler manifold of arbitrary dimension. We provide local in time regular solutions, which can be extended to global bounded ones if the data of the problem are small.     

Quantization of complex Lagrangian submanifolds

Let Λ be a smooth Lagrangian submanifold of a complex symplectic manifold X. We construct twisted simple holonomic modules along Λ in the stack of deformation-quantization modules on X.     

On cellularization for simplicial presheaves and motivic homotopy

We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss applications to the motivic homotopy category of Morel and Voevodsky.     

QN-spaces, wQN-spaces and covering properties

The main results of the paper are as follows: covering characterizations of wQN-spaces, covering characterizations of QN-spaces and a theorem saying that Cp(X) has the Arkhangel'ski?ˇ property (α₁) provided that X is a QN-space. The latter statement solves a problem posed by M. Scheepers [M. Scheepers, Cp(X) and Arhangel'ski?ˇ's αi-spaces, Topology Appl. 89 (1998) 265-275] and for Tychonoff spaces was independently proved by M. Sakai [M. Sakai, The sequence selection properties of Cp(X), Preprint, April 25, 2006]. As the most interesting result we consider the equivalence that a normal topological space X is a wQN-space if and only if X has the property S₁(Γshr,Γ). Moreover we show that X is a QN-space if and only if Cp(X) has the property (α₀), and for perfectly normal spaces, if and only if X has the covering property (β₃).     

An adaptive scheme for the approximation of dissipative systems

We propose a new scheme for the long time approximation of a diffusion when the drift vector field is not globally Lipschitz. Under this assumption, a regular explicit Euler scheme–with constant or decreasing step–may explode and implicit Euler schemes are CPU-time expensive. The algorithm we introduce is explicit and we prove that any weak limit of the weighted empirical measures of this scheme is a stationary distribution of the stochastic differential equation. Several examples are presented including gradient dissipative systems and Hamiltonian dissipative systems.     

A delta white noise functional

The additive renormalization% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabs7adaWgaaWcbaGaaeySdiaab6cacaqG0bqefeKCPfgBaGqb% diaa-bcaaeqaaOGaeyypa0Jaa8hiaiaacIcacaaIYaGaeqiWdaNaai% ykamaaCaaaleqabaGaeyOeI0IaaGymaiaac+cacaaIYaaaaGqadOGa% a4hiaiGacwgacaGG4bGaaiiCaiaacIcacqGHsislcaqGXoWaaWbaaS% qabeaacaqGYaaaaOGaai4laiaaikdacaGGPaGaa4hiaiaacQdaciGG% LbGaaiiEaiaacchacqGHXcqSdaWadiqaaiabgkHiTiaadkeacaGGNa% GaaiikaiaadshacaGGPaWaaWbaaSqabeaacaaIYaaaaOGaai4laiaa% ikdacaGFGaGaey4kaSIaa4hiaiaabg7acaWGcbGaai4jaiaacIcaca% WG0bGaaiykaaGaay5waiaaw2faaiaacQdaaaa!6C5C!\[{\rm{\delta }}_{{\rm{\alpha }}{\rm{.t}} } = (2\pi )^{ - 1/2} \exp ( - {\rm{\alpha }}^{\rm{2}} /2) :\exp \pm \left[ { - B'(t)^2 /2 + {\rm{\alpha }}B'(t)} \right]:\]is shown to be a generalized Brownian functional. Some of its properties are derived. is shown to be a generalized Brownian functional. Some of its properties are derived.On leave from Universidade do Minho, Area de Matematica, Largo Carlos Amarante, P-4700 Braga, Portugal.     

On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k × k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

The problem of Dirichlet for anisotropic quasilinear degenerate elliptic equations

We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results are new even in the semilinear case when the principal part is the Laplace operator.