Related papers: The stochastic Weiss conjecture for bounded analyt…

In this paper we extend an inequality of Lenglart, L\'epingle and Pratelli \cite[Lemma 1.1]{LLP} to general continuous adapted stochastic processes with values in topology spaces. By this inequality we show Burkholder-Davies-Gundy's…

In this paper we consider the general fractional equation \sum_{j=1}^m \lambda_j \frac{\partial^{\nu_j}}{\partial t^{\nu_j}} w(x_1,..., x_n ; t) = -c^2 (-\Delta)^\beta w(x_1,..., x_n ; t), for \nu_j \in (0,1], \beta \in (0,1] with initial…

In this paper, we consider the following Cauchy problem of \begin{equation*} \left\{ \begin{array}{lll} iu_t=\Delta u+2\delta_huh'(|u|^2)\Delta h(|u|^2)+V(x)u+F(|u|^2)u+(W*|u|^2)u,\ x\in \mathbb{R}^N,\ t>0\\ u(x,0)=u_0(x),\quad x\in…

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $\left(\varphi_1, \varphi_2\right)-$convex function $g, $ with arbitrarily small norm, such that $f + g…

We introduce the vertical \(\widehat{A}\)-cowaist, a codimension-one invariant for partitioned manifolds. It extends the concept of infinite vertical \(\widehat{A}\)-cowaist for bands to arbitrary partitioned manifolds, which may be…

The Cauchy problem for second order linear differential equation $u''(t)+Du'(t)+Au(t)=0$ in Hilbert space $H$ with a sectorial operator $A$ and an accretive operator $D$ is studied. Sufficient conditions for exponential decay of the…

Let ${\mathcal B}(H)$ denote the Banach algebra of all bounded linear operators on a complex Hilbert space $H$ with $\dim H\geq 3$, and let $\mathcal A$ and $\mathcal B$ be subsets of ${\mathcal B}(H)$ which contain all rank one operators.…

The parabolic integro-differential Cauchy problem with spatially dependent coefficients is considered in generalized Bessel potential spaces where smoothness is defined by L\'evy measures with O-regularly varying profile. The coefficients…

A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…

Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. \ It is proved that every separable metric space admits a metric $\mathcal{M}_d$-frame.…

We derive Onsager-Machlup functionals for countable product measures on weighted $\ell^p$ subspaces of the sequence space $\mathbb{R}^{\mathbb{N}}$. Each measure in the product is a shifted and scaled copy of a reference probability measure…

We present a versatile framework to study strong existence and uniqueness for stochastic differential equations (SDEs) in Hilbert spaces with irregular drift. We consider an SDE in a separable Hilbert space $H$ \begin{equation*} dX_t= (A…

In this paper we investigate the long-time behavior of stochastic reaction-diffusion equations of the type $du = (Au + f(u))dt + \sigma(u) dW(t)$, where $A$ is an elliptic operator, $f$ and $\sigma$ are nonlinear maps and $W$ is an infinite…

We prove a sharp bound for the minimal doubling of a small measurable subset of a compact connected Lie group. Namely, let $G$ be a compact connected Lie group of dimension $d_G$, we show that for for all measurable subsets $A$, we have…

For a mixed stochastic differential equation containing both Wiener process and a H\"older continuous process with exponent $\gamma>1/2$, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of…

This note deals with existence and uniqueness of (variational) solutions to the following type of stochastic partial differential equations on a Hilbert space H dX(t) = A(t,X(t))dt + B(t,X(t))dW(t) + h(t) dG(t) where A and B are random…

The twice-dimensionally reduced Seiberg-Witten monopole equations admit solutions depending on two real parameters (b,c) and an arbitrary analytic function f(z) determining a solution of Liouville's equation. The U(1) and manifold curvature…

We prove that for every semigroup of Schwarz maps on the von~Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space…

We establish necessary and sufficient conditions for stochastic invariance of closed subsets in Hilbert spaces for solutions to infinite-dimensional stochastic differential equations (SDEs) under mild assumptions on the coefficients. Our…

We obtain in closed form averages of polynomials, taken over hermitian matrices with the Gaussian measure involved in the Kontsevich integral, and prove a conjecture of Witten enabling one to express analogous averages with the full (cubic…