Asymptotic stability in L¹ of a transport equation
We study the asymptotic behaviour of solutions of a transport equation. We give some sufficient conditions for the complete mixing property of the Markov semigroup generated by this equation.
Asymptotic stability of a linear Boltzmann-type equation
We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon-Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon-Wu equation is given.
Asymptotic stability of a partial differential equation with an integral perturbation
We study the asymptotic behaviour of the Markov semigroup generated by an integro-partial differential equation. We give new sufficient conditions for asymptotic stability of this semigroup.
Asymptotic stability of a repairable system with imperfect switching mechanism.
Asymptotic variance of functionals of discrete-time Markov chains via the Drazin inverse.
Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions
Asymptotic windings of planar brownian motion revisited via the Ornstein-Uhlenbeck process
Asymptotic windings over the trefoil knot.
Consider the group G:=PSL2(R) and its subgroups Γ:= PSL2(Z) and Γ':=DSL2(Z). G/Γ is a canonical realization (up to an homeomorphism) of the complement S3T of the trefoil knot T, and G/Γ' is a canonical realization of the 6-fold branched cyclic cover of S3T, which has a 3-dimensional cohomology of 1-forms.Putting natural left-invariant Riemannian metrics on G, it makes sense to ask which is the asymptotic homology performed by the Brownian motion in G/Γ', describing thereby in an intrinsic way part...
Asymptotical mean square stability of Cohen-Grossberg neural networks with random delay.
Asymptotically optimal filtering in linear systems with fractional Brownian noises.
In this paper, the filtering problem is revisited in the basic Gaussian homogeneous linear system driven by fractional Brownian motions. We exhibit a simple approximate filter which is asymptotically optimal in the sense that, when the observation time tends to infinity, the variance of the corresponding filtering error converges to the same limit as for the exact optimal filter.
Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces*
We describe quantization designs which lead to asymptotically and order optimal functional quantizers for Gaussian processes in a Hilbert space setting. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a constructive quantization scheme we rely on the knowledge of the eigenvectors of the covariance operator in order to transform the problem into a finite dimensional quantization problem of normal distributions. ...
Asymptotics for an arcsin type result
Asymptotics for conservation laws involving Lévy diffusion generators
Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.
Asymptotics for general nonstationary fractionally integrated processes without prehistoric influence.
Asymptotics for open-loop window flow control.
Asymptotics for Products of a Random Number of Partial Sums
We consider products of a random number of partial sums of independent, identically distributed, positive square-integrable random variables. We show that the distribution of these products is asymptotically lognormal.
Asymptotics for products of sums and -statistics.
Asymptotics for random walks in alcoves of affine Weyl groups.
Asymptotics for random walks with dependent heavy-tailed increments.
Asymptotics for rooted bipartite planar maps and scaling limits of two-type spatial trees.