Relevant bibliographies by topics / Symmetric diffusion semigroups

Academic literature on the topic 'Symmetric diffusion semigroups'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Symmetric diffusion semigroups"

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Wu, Liming. "Two Inequalities for Symmetric Diffusion Semigroups underΓ3⩾0." Journal of Functional Analysis 175, no. 2 (August 2000): 393–414. http://dx.doi.org/10.1006/jfan.2000.3603.

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Chen, Zhen-Qing, Zhongmin Qian, Yaozhong Hu, and Weian Zheng. "Stability and Approximations of Symmetric Diffusion Semigroups and Kernels." Journal of Functional Analysis 152, no. 1 (January 1998): 255–80. http://dx.doi.org/10.1006/jfan.1997.3147.

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Xu, Quanhua. "Vector-valued Littlewood-Paley-Stein Theory for Semigroups II." International Mathematics Research Notices 2020, no. 21 (September 17, 2018): 7769–91. http://dx.doi.org/10.1093/imrn/rny200.

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Abstract Inspired by a recent work of Hytönen and Naor, we solve a problem left open in our previous work joint with Martínez and Torrea on the vector-valued Littlewood-Paley-Stein theory for symmetric diffusion semigroups. We prove a similar result in the discrete case, namely, for any $T$ which is the square of a symmetric diffusion Markovian operator on a measure space $(\Omega , \mu )$. Moreover, we show that $T\otimes{ \textrm{Id}}_X$ extends to an analytic contraction on $L_p(\Omega ; X)$ for any $1<p<\infty $ and any uniformly convex Banach space $X$.
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Kim, Panki, and Renming Song. "Intrinsic ultracontractivity of non-symmetric diffusion semigroups in bounded domains." Tohoku Mathematical Journal 60, no. 4 (2008): 527–47. http://dx.doi.org/10.2748/tmj/1232376165.

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Chen, Zhen-Qing, and Xicheng Zhang. "Heat kernels and analyticity of non-symmetric jump diffusion semigroups." Probability Theory and Related Fields 165, no. 1-2 (May 10, 2015): 267–312. http://dx.doi.org/10.1007/s00440-015-0631-y.

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Jabeen, Tahira, Ravi P. Agarwal, Vasile Lupulescu, and Donal O’Regan. "Impulsive Evolution Equations with Causal Operators." Symmetry 12, no. 1 (December 25, 2019): 48. http://dx.doi.org/10.3390/sym12010048.

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In this paper, we establish sufficient conditions for the existence of mild solutions for certain impulsive evolution differential equations with causal operators in separable Banach spaces. We rely on the existence of mild solutions for the strongly continuous semigroups theory, the measure of noncompactness and the Schauder fixed point theorem. We consider the impulsive integro-differential evolutions equation and impulsive reaction diffusion equations (which could include symmetric kernels) as applications to illustrate our main results.
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Li, Huaiqian, Dejun Luo, and Jian Wang. "Harnack inequalities for SDEs with multiplicative noise and non-regular drift." Stochastics and Dynamics 15, no. 03 (May 22, 2015): 1550015. http://dx.doi.org/10.1142/s021949371550015x.

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The log-Harnack inequality and Harnack inequality with powers for semigroups associated to SDEs with non-degenerate diffusion coefficient and non-regular time-dependent drift coefficient are established, based on the recent papers [7, 21]. We consider two cases in this work: (1) the drift fulfills the LPS-type integrability, and (2) the drift is uniformly Hölder continuous with respect to the spatial variable. Finally, by using explicit heat kernel estimates for the stable process with drift, the Harnack inequality for the stochastic differential equation driven by symmetric stable process is also proved.
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FITZSIMMONS, P. J. "DRIFT TRANSFORMATIONS OF SYMMETRIC DIFFUSIONS, AND DUALITY." Infinite Dimensional Analysis, Quantum Probability and Related Topics 10, no. 04 (December 2007): 613–31. http://dx.doi.org/10.1142/s0219025707002890.

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Starting with a symmetric Markov diffusion process X (with symmetry measure m and L2 (m) infinitesimal generator A) and a suitable core [Formula: see text] for the Dirichlet form of X, we describe a class of derivations defined on [Formula: see text]. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov's theorem. The transformed process XB is typically non-symmetric, but we are able to show that if the "divergence" of B is positive, then m is an excessive measure for XB, and the L2 (m) infinitesimal generator of XB is an extension of f ↦ Af + B (f). The methods used are mainly probabilistic, and involve the notions of even and odd continuous additive functionals, and Nakao's stochastic divergence. These methods yield a probabilistic approach to the adjoint of the semigroup of XB, and in particular lead to a solution of a problem of W. Stannat.
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Tong, Zhigang, and Allen Liu. "Analytical pricing formulas for discretely sampled generalized variance swaps under stochastic time change." International Journal of Financial Engineering 04, no. 02n03 (June 2017): 1750028. http://dx.doi.org/10.1142/s2424786317500281.

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We propose a new class of models for pricing generalized variance swaps. We assume that, in the most general form, the process for the asset price is a function of a general time-homogeneous diffusion process belonging to a symmetric pricing semigroup, time changed by a composition of a Lévy subordinator and an absolutely continuous process. We derive the analytical pricing formulas for various types of generalized variance swaps based on eigenfunction expansion method. We also numerically implement the model and test its sensitivity to some of the key parameters of the model.
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Goldberg, Maxim J., and Seonja Kim. "A Natural Diffusion Distance and Equivalence of Local Convergence and Local Equicontinuity for a General Symmetric Diffusion Semigroup." Abstract and Applied Analysis 2018 (October 2, 2018): 1–9. http://dx.doi.org/10.1155/2018/6281504.

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In this paper, we consider a general symmetric diffusion semigroup Ttft≥0 on a topological space X with a positive σ-finite measure, given, for t>0, by an integral kernel operator: Ttf(x)≜∫X‍ρt(x,y)f(y)dy. As one of the contributions of our paper, we define a diffusion distance whose specification follows naturally from imposing a reasonable Lipschitz condition on diffused versions of arbitrary bounded functions. We next show that the mild assumption we make, that balls of positive radius have positive measure, is equivalent to a similar, and an even milder looking, geometric demand. In the main part of the paper, we establish that local convergence of Ttf to f is equivalent to local equicontinuity (in t) of the family Ttft≥0. As a corollary of our main result, we show that, for t0>0, Tt+t0f converges locally to Tt0f, as t converges to 0+. In the Appendix, we show that for very general metrics D on X, not necessarily arising from diffusion, ∫X‍ρt(x,y)D(x,y)dy→0 a.e., as t→0+. R. Coifman and W. Leeb have assumed a quantitative version of this convergence, uniformly in x, in their recent work introducing a family of multiscale diffusion distances and establishing quantitative results about the equivalence of a bounded function f being Lipschitz, and the rate of convergence of Ttf to f, as t→0+. We do not make such an assumption in the present work.
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Dissertations / Theses on the topic "Symmetric diffusion semigroups"

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Taggart, Robert James Mathematics &amp Statistics Faculty of Science UNSW. "Evolution equations and vector-valued Lp spaces: Strichartz estimates and symmetric diffusion semigroups." 2008. http://handle.unsw.edu.au/1959.4/43298.

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The results of this thesis are motivated by the investigation of abstract Cauchy problems. Our primary contribution is encapsulated in two new theorems. The first main theorem is a generalisation of a result of E. M. Stein. In particular, we show that every symmetric diffusion semigroup acting on a complex-valued Lebesgue space has a tensor product extension to a UMD-valued Lebesgue space that can be continued analytically to sectors of the complex plane. Moreover, this analytic continuation exhibits pointwise convergence almost everywhere. Both conclusions hold provided that the UMD space satisfies a geometric condition that is weak enough to include many classical spaces. The theorem is proved by showing that every symmetric diffusion semigroup is dominated by a positive symmetric diffusion semigoup. This allows us to obtain (a) the existence of the semigroup's tensor extension, (b) a vector-valued version of the Hopf--Dunford--Schwartz ergodic theorem and (c) an holomorphic functional calculus for the extension's generator. The ergodic theorem is used to prove a vector-valued version of a maximal theorem by Stein, which, when combined with the functional calculus, proves the pointwise convergence theorem. The second part of the thesis proves the existence of abstract Strichartz estimates for any evolution family of operators that satisfies an abstract energy and dispersive estimate. Some of these Strichartz estimates were already announced, without proof, by M. Keel and T. Tao. Those estimates which are not included in their result are new, and are an abstract extension of inhomogeneous estimates recently obtained by D. Foschi. When applied to physical problems, our abstract estimates give new inhomogeneous Strichartz estimates for the wave equation, extend the range of inhomogeneous estimates obtained by M. Nakamura and T. Ozawa for a class of Klein--Gordon equations, and recover the inhomogeneous estimates for the Schr??dinger equation obtained independently by Foschi and M. Vilela. These abstract estimates are applicable to a range of other problems, such as the Schr??dinger equation with a certain class of potentials.
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Conference papers on the topic "Symmetric diffusion semigroups"

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Balas, Mark J., and Susan A. Frost. "A Stabilization of Fixed Gain Controlled Infinite Dimensional Systems by Augmentation With Direct Adaptive Control." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3726.

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Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.
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