‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

We consider the regularity of solutions for some parabolic equations. We show Hölder continuity with exponent (1 + α)/2, with respect to the time variable, when the gradient in the space variable of the solution has the Hölder continuity with exponent α.

For Hölder continuous cocycles over an invertible, Lipschitz base, we establish the Hölder continuity of Oseledets subspaces on compact sets of arbitrarily large measure. This extends a result of Araújo et al [On Hölder-continuity of Oseledets subspaces J. Lond. Math. Soc. 93 (2016) 194–218] by considering possibly non-invertible cocycles, which, in addition, may take values in the space of com...

For Hölder cocycles over a Lipschitz base transformation, possibly noninvertible, we show that the subbundles given by the Oseledets Theorem are Höldercontinuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmüller flow on the moduli space of abelian differentials. Following a recen...

In this note, we shall investigate the Hölder continuity of matrix functions applied to normal matrices provided that the underlying scalar function is Hölder continuous. Furthermore, a few examples will be given.

Abstract. We show that for each weakly majorizing measure there is a natural metric with respect to which sample paths of stochastic processes are Hölder continuous and their Hölder norm satisfies a strong integrability condition. We call such metric a minorizing metric. The class of minorizing metrics is minimal among all metrics assuring sample Hölder continuity of processes satisfying certai...

This paper relates uniform α-Hölder continuity, or α-dimensionality, of spectral measures in an arbitrary interval to the Fourier transform of the measure. This is used to show that scaling exponents of exponential sums obtained from time series give local upper bounds on the degree of Hölder continuity of the power spectrum of the series. The results have applications to generalized random wal...

In this paper we consider a broad class of distributionally robust optimization (DRO for short) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is defined through parametric moment conditions with generic cone constraints. Under some moderate conditions including Slater type conditions of cone constrained moment system an...