Matyas Barczy, Gyula Pap
We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
A Self-Contained Proof of the Portmanteau Theorem
本文以七条陈述形式统一证明Portmanteau定理，强调有界连续函数期望与开闭集概率界的蕴含循环，并阐明中间函数类的作用。
Here we obtain the exact asymptotics for large and moderate deviations, strong law of large numbers and central limit theorem for chains with unbounded variable length memory.
We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator $g$ allowing a general growth in the state variable $y$ and a sub-quadratic growth in the state variable $z$, like $|z|^α$ for some $α\in (1,2)$, when the terminal condition satisfies a sub-exponential moment integrability condition like $\exp\left(μL^{2/α^*}\right)$ for the conjugate $α^*$ of $α$ and a positive parameter $μ>μ_0$ with a certain value $μ_0$, which is clearly weaker than the usual $\exp(μL)$ integrability and stronger than $L^p\ (p>1)$ integrability. The…
We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched local central limit theorem for $X$, under some moment conditions on the environment; the key tool is a local parabolic Harnack inequality obtained with Moser iteration technique.
We compute some dependence coefficients for the stationary Markov chain whose transition kernel is the Perron-Frobenius operator of an expanding map $T$ of $[0, 1]$ with a neutral fixed point. We use these coefficients to prove a central limit theorem for the partial sums of $f\circ T^i$, when $f$ belongs to a large class of unbounded functions from $[0, 1]$ to ${\mathbb R}$. We also prove other limit theorems and moment inequalities.
Three central limit theorems for the unbounded excursion component of a Gaussian field
本文研究了高斯场中无界游走部分的体积、表面积和欧拉特征的中心极限定理，揭示了临界水平与超临界水平下的统计性质。
Existence, uniqueness and comparison theorem on unbounded solutions of general time interval BSDEs with sub-quadratic generators
本文研究一般时间区间上具有次二次生成元的一维BSDEs，在时变增长条件下证明无界解的存在性、唯一性与比较定理，并提出若干首次探索的唯一性充分条件。
We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic ows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of [5]
We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endowment. To obtain this duality, we prove a robust version of Rockafellar's theorem on convex integral functionals and apply Fenchel's general duality theorem.
This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of a scalar backward stochastic differential equation (BSDE) whose generator grows (with respect to both unknown variables $y$ and $z$) in a super-linear way like $|y||\ln |y||^{(λ+1/2)\wedge 1}+|z||\ln |z||^λ$ for some $λ\geq 0$. For the following four different ranges of the growth power parameter $λ$: $λ=0$, $λ\in (0,1/2)$, $λ=1/2$ and $λ>1/2$, we give reasonably weakest possible different integrability conditions of the terminal value for the existence of an unbounded solution to the BSDE. In t…
Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for inhomogeneous diffusion processes with unbounded drift and diffusion coefficients by using the Schauder estimates for partial differential equations of parabolic type and the theory of weakly continuous semigroups. The FDTs proved in this paper apply to any forms of inhomogeneous and nonlinear external perturbations. Furthermore, we prove the uniqueness of the co…
Local Central Limit Theorem for unbounded long-range potentials
本文证明了格点上长程相互作用两体势的积分中心极限定理与局部中心极限定理的等价性，利用集团展开和稀释技术分别处理无界与有界自旋情形。
Nevai's condition for measures with unbounded supports
本文研究了具有无界支持的测度中Nevai条件的适用性，并展示了其在Christoffel-Darboux核渐进行为和极限定理中的应用。
In this paper, we prove a central limit theorem and establish a moderate deviation principle for 2D stochastic hydrodynamical type systems with multiplicative noise in unbounded domains, which covers 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic B?enard problem and also shell models of turbulence. The weak convergence method plays an important role in obtaining the moderate deviation principle.
In this paper we consider two classes of backward stochastic differential equations. Firstly, under a Lipschitz-type condition on the generator of the equation, which can also be unbounded, we give sufficient conditions for the existence of a unique solution pair. The method of proof is that of Picard iterations and the resulting conditions are new. We also prove a comparison theorem. Secondly, under the linear growth and continuity assumptions on the possibly unbounded generator, we prove the existence of the solution pair. This class of equations is more general than the existing ones.
Stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains driven by a multiplicative Gaussian noise are considered. The noise term depends on the unknown velocity and its spatial derivatives. The existence of a martingale solution is proved. The construction of the solution is based on the classical Faedo-Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod Theorem for non-metric spaces. Moreover, some compactness and tightness criteria in non-metric spaces are proved. Compactness results are based on a certain generalization of the classi…
Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and mathematical finance, concerning degenerate diffusion processes. We show that the martingale problem associated with a degenerate-elliptic differential operator with unbounded, locally Holder continuous coefficients on a half-space is well-posed in the sense of Stroock and Varadhan. Second, we prove existence, uniqueness, and the strong Markov property for w…
Martingale solutions of stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains, driven by the Lévy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered. Using the classical Faedo-Galerkin approximation and the compactness method we prove existence of a martingale solution. We prove also the compactness and tighness criteria in a certain space contained in some spaces of càdlàg functions, weakly càdlàg functions and some Fréchet spaces. Moreover, we use a version of the Skorokhod Embedding Theorem for nonmetric spa…
Pullback measure attractors for non-autonomous stochastic FitzHugh-Nagumo system with distribution dependence on unbounded domains
本文研究无界域上依赖分布的非自治随机 FitzHugh-Nagumo 系统，基于 Banach 不动点定理证明解的适定性，并结合分裂技巧、尾端估计与 Vitali 定理证明拉回测度吸引子的存在唯一性。
In this dissertation, we show that the Central Limit Theorem and the Invariance Principle for Discrete Fourier Transforms discovered by Peligrad and Wu can be extended to the quenched setting. We show that the random normalization introduced to extend these results is necessary and we discuss its meaning. We also show the validity of the quenched Invariance Principle for fixed frequencies under some conditions of weak dependence. In particular, we show that this result holds in the martingale case. The discussion needed for the proofs allows us to show some general facts apparently not noticed…
In this paper a quantum stochastic integral representation theorem is obtained for unbounded regular martingales with respect to multidimensional quantum noise. This simultaneously extends results of Parthasarathy and Sinha to unbounded martingales and those of the author to multidimensions.
In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vectors correspond to the moments of the Marchenko-Pastur distribution and Wigner's semi-circle law.
Invariant measures for stochastic Burgers equation in unbounded domains with space-time white noise
本文研究全实轴上带乘性时空白噪声的随机阻尼Burgers方程，证明了加权空间中温和解的存在唯一性与依概率有界性，并借助Krylov-Bogolioubov定理得到了不变测度的存在性。
In this paper we find necessary and sufficient conditions for the weak convergence of c-free convolution of pairs of measures, where the measures are assumed to be infinitesimal and their support may be unbounded. These results are obtained by complex analytic methods.
A Chung--Fuchs type theorem for skew-product dynamical systems
本文证明斜积动力系统的Chung--Fuchs型定理，给出Birkhoff和无界与振荡的条件，并应用于Mandelbrot级联在临界情形的退化性。
We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in "An operad of non-commutative independences defined by trees" (Dissertationes Mathematicae, 2020, doi:10.4064/dm797-6-2020), which generalize the free, boolean, monotone, and orthogonal convolutions. In particular, for each rooted subtree $\mathcal{T}$ of the $N$-regular tree (with vertices labeled by alternating strings), we define the convolution $\boxplus_{\mathcal{T}}(μ_1,\dots,μ_N)$ for arbitrary probability measures $μ_1$, ..., $μ_N$ on $\mathbb{R}$ using a certain fixed-poin…
The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN). A rather precise rate of convergence is given both for LLN and CLT.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。