In this article, we prove uniqueness and energy balance for isentropic Euler system driven by a cylindrical Wiener process. Pathwise result is obtained weak solutions having Hölder regularity C α , > 1 ∕ 2 in space satisfying one-sided Lipschitz bound on velocity. We Onsager’s conjecture with stochastic forcing, that is, equation enjoying 3 . Both the results have been more general setting cons...

In this paper we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C open sets in R, where d ≥ 1 and α ∈ (1, 2). We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functio...

We consider the problem of fixed-interval smoothing of a continuous-time partially observed nonlinear stochastic dynamical system. Existing results for such smoothers require the use of two-sided stochastic calculus. The main contribution of this paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the smoothing equations are nonstochastic paraboli...

‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.