For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measuretheoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the exist...

The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacem...

We address the distinction between dynamical and additive noise in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low levels of the latter and high levels of the former indicate the presence of dynamical noise only, while low values of the two are observed as soon as additive ...

φ f (x) =   f (x)− f (x0) x−x0 , x , x0 f ′(x0), x = x0. Now, by the differentiability of f at x0, we have lim x→x0 x∈X\{x0 } φ f (x) = lim x→x0 x∈X\{x0 } f (x) − f (x0) x − x0 = f (x0) = φ f (x0). This proves that φ f is continuous at x0. Moreover, (1.1) holds for all x ∈ X by definition of φ f . ((1.1) is clearly true when x , x0. When x = x0, both sides of (1.1) are zero.) Therefore (ii) ...

Let M and L be elliptic differential operators of orders 2m and 2/, respectively, with m ̂ S. The existence and uniqueness of a solution to the abstract mixed initial and boundary value problem Mu(t) + Lu(t) = 0, u(0) = u0 was established for u0 given in the domain of the infinitesimal generator of a strongly-continuous semi-group. The purpose of this paper is to show that this semi-group is hol...

We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are based on a notion of pathwise functional derivative and yield a consistent estimator for the integrand in the martingale representation formula for any square-integrable functional of the solution of an SDE with path-dependent coeff...

Assumptions on a likelihood function, including a local GlivenkoCantelli condition, imply the existence of M-estimators converging to an Mfunctional. Scatter matrix-valued estimators, defined on all empirical measures on R for d ≥ 2, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they...

In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a Hölder continuous function with parameter greater that 1/2 via the Young integration setting. Then some estimates of the solution are obtained, which allow to show that the solution of a delay differential equation driven by a fractional Brownian motion (fBm) with Hurst...

In this paper, we aim to explore properties of a class of NCP-functions and investigate a related semismooth Newton method for complementarity problems. Some favorite properties about the class of NCP-functions and its merit function are discussed including strong semismoothness, continuous differentiability and the nonsingularity of the element in C-subdifferential. In particular, we present a...

The main result is an improvement of previous results on the equation f(x) + f(y)− f(x+ y) = g[φ(x) + φ(y)− φ(x+ y)] for a given function φ. We find its general solution assuming only continuous differentiability and local nonlinearity of φ. We also provide new results about the more general equation f(x) + f(y)− f(x+ y) = g(H(x, y)) for a given function H. Previous uniqueness results required ...