Abstract This note presents an estimator of the hazard rate function based on right censored data. A collection of estimators is built from a regression-type contrast, in a general collection of linear models. Then, a penalised model selection procedure provides an estimator which satisfies an oracle inequality. In particular, we can prove that it is adaptive in the minimax sense on Hölder spaces.

These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations. MSC. 35K55, 35D40, ...

We consider a Lévy process in Rd (d ≥ 3) with the characteristic exponent Φ(ξ) = |ξ|2 ln(1 + |ξ|2) − 1. The scale invariant Harnack inequality and apriori estimates of harmonic functions in Hölder spaces are proved. AMS Subject Classification: Primary 60J45, Secondary 60G50, 60G51, 60J25, 60J27

Abstract We will show the Cheeger–Colding segment inequality for manifolds with integral Ricci curvature bound. By using this inequality, almost rigidity structure results be derived by a similar method as in [1]. And sharp Hölder continuity result of [7] holds limit space

In this work, we investigate the tensor inequalities in t-product formalism. The involving power are proved to hold similarly as standard matrix scenarios. We then focus on norm inequalities. well-known arithmetic-geometric mean inequality, Hölder and Minkowski inequality generalized tensors. Furthermore, obtain some t-eigenvalue

In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using To be more precise, obtained taking advantage of the convexity, Hölder inequality, and power mean inequality. Furthermore, previous new results presented special cases theorems.

By constructing a coupling with unbounded time-dependent drift, lower bound estimate of dimension-free Harnack inequality power is obtained for large class stochastic differential equation multiplicative noise. The key an application the inverse Hölder inequality. Combining this well-known upper bound, bilateral established. As dual inequality, shift-Harnack inequalities are also investigated a...