Related papers: On hypoellipticity of degenerate operators in test…

Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles. However, generative models have limited capacity to handle rich sensory…

Multidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. In this paper we…

Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing. The previous studies assume that the potential source is completely…

Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…

We prove estimates for the stationary state $n$-point functions at zero molecular diffusivity in the Kraichnan model. This is done by proving upper bounds for the heat kernels and Green's functions of the degenerate elliptic operators $M_n$…

A scheme for the detection of low-intensity optical coherent signals was studied which uses a probabilistic amplifier operated in the non-heralded version, as the underlying non-linear operation to improve the detection efficiency. This…

We consider a class of non-trivial perturbations ${\mathscr A}$ of the degenerate Ornstein-Uhlenbeck operator in ${\mathbb R}^N$. In fact we perturb both the diffusion and the drift part of the operator (say $Q$ and $B$) allowing the…

This article presents an investigation on the global hypoellipticity problem for systems belonging to the class $P = D_t + Q(t,D_x)$, where $Q(t,D_x)$ is a $m\times m$ matrix with entries $c_{j,k}(t)Q_{j,k}(D_x)$. The coefficients…

We study the small-time asymptotics for hypoelliptic diffusion processes conditioned by their initial and final positions, in a model class of diffusions satisfying a weak H\"ormander condition where the diffusivity is constant and the…

Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of…

This paper revisits the previously proposed linear asymptotic observer of the motion state variables with nonlinear friction and provides a robust design suitable for both, transient presliding and steady-state sliding phases of the…

We find operators distinguishing the degenerate states for the Hamiltonian $H= x(K+{1/2})S_z +{\bf K}\cdot {\bf S}$ at $x=\pm 1$ that was given by Happer et al$^{[1,2]}$ to interpret the curious degeneracies of the Zeeman effect for…

This paper defines a novel Bayesian inverse problem to infer an infinite-dimensional uncertain operator appearing in a differential equation, whose action on an observable state variable affects its dynamics. Inference is made tractable by…

We study the long-time behaviour of the first-moment semigroup of a non conservative piecewise deterministic measure-valued stochastic process with support on R 2 + driven by a deterministic flow between random jump times, with a transition…

In this paper, we study the hypocoercivity for a class of linear kinetic equations with both transport and degenerately dissipative terms. As concrete examples, the relaxation operator, Fokker-Planck operator and linearized Boltzmann…

We numerically investigate the transport properties of interacting spinless electrons in disordered systems. We use an efficient method which is based on the diagonalization of the Hamiltonian in the subspace of the many-particle Hilbert…

We prove H\"ormander's type hypoellipticity theorem for stochastic partial differential equations when the coefficients are only measurable with respect to the time variable. The need for such kind of results comes from filtering theory of…

We study the `asymmetric' Hubbard model, where hoppings of electrons depend on their spin. For strong interactions and sufficiently asymmetric hoppings, it is proved that the ground state displays phase separation away from half-filling.…

In this paper, we study the homogenization of a diffusion process with jumps, that is, Feller process generated by an integro-differential operator. This problem is closely related to the problem of homogenization of boundary value problems…

This paper addresses the problem of distributed hypothesis testing in multi-agent networks, where agents repeatedly collect local observations about an unknown state of the world, and try to collaboratively detect the true state through…