In this paper, we study the least concave majorant of a stochastic process, and more precisely the set of times where its slope varies, which we call the extremal superior times. We establish the negligibility of this set, namely the extremal superior set, for certain classes of processes, including Lévy processes, their integrated processes, and Itô processes. We examine more closely the case ...

Kurdyka–?ojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL $$\frac{1}{2}$$ for suitable potential function is related to local linear convergence. Nevertheless, general extremely hard estimate. this paper, we show under mild assumptions that preserved via inf-projection. Inf-projection fundamental op...

Monte-Carlo approach towards solving Cauchy problem for large systems of linear differential equations is being proposed in this paper. Firstly, a quick overlook previously obtained results from applying the Fredholm-type integral made. In main part paper, similar method applied system ODE. It transformed into an equivalent Volterra-type equations, which relaxes certain limitations present due ...

This article proposes an omnibus test for monotonicity of nonparametric conditional distributions and its moments. Unlike previous proposals, our method does not require smooth estimation of the derivatives of nonparametric curves and it can be implemented even when probability densities do not exist. In fact, we only require continuity of the marginal distributions under the null and fixed alt...

We consider the problem of studying sensitivity ellipsoidal frequency estimates quality multivariable dynamic systems to parameter variations. To solve problem, we use apparatus functions extreme elements singular value decomposition real-valued transfer matrices. The joint usage with method state space allowed us construct models sensitivity. On basis obtained models, for state, output and err...