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Remarks on global hypoellipticity [PDF]
Transactions of the American Mathematical Society, 1973 We study differential operators D which commute with a fixed normal elliptic operator E on a compact manifold M. We use eigenfunction expansions relative to E to obtain simple conditions giving global hypoellipticity. These conditions are equivalent to D having parametrices in certain spaces of functions or distributions.
Greenfield, Stephen J. +1 more
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Time regularity for generalized Mehler semigroups
Mathematische Nachrichten, Volume 295, Issue 11, Page 2223-2245, November 2022., 2022 Abstract We study continuity and Hölder continuity of t↦Ptf$t\mapsto P_tf$, where Pt$P_t$ is a generalized Mehler semigroup in Cb(X)$C_b(X)$, the space of the continuous and bounded functions from a Banach space X to R$\mathbb {R}$, and f∈Cb(X)$f\in C_b(X)$.
Alessandra Lunardi
wiley +1 more source
Manifold Markov chain Monte Carlo methods for Bayesian inference in diffusion models
Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 84, Issue 4, Page 1229-1256, September 2022., 2022 Abstract Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology—borrowing ideas from statistical physics and computational chemistry—for ...
Matthew M. Graham +2 more
wiley +1 more source
On differential operators an differential equations on torus
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2018 In this paper, we consider periodic boundary value problems for a differential equation whose coefficients are trigonometric polynomials. The spaces of generalized functions are constructed, in which the problems considered have solutions, in particular,
Vladimir P Burskii
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Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 The main aim of this survey article is to present several known results about vector‐valued almost periodic functions and their applications. We separately consider almost periodic functions depending on one real variable and almost periodic functions depending on two or more real variables.
Wei-Shih Du +3 more
wiley +1 more source
Electronic Communications in Probability, 2016 We prove that if the Markov generator of a diffusion process satisfies the two step strong H rmander condition, the conditioned hypoelliptic bridge satisfies an integral bound and is a continuous semi-martingale.
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Analytic Hypoellipticity and the Treves Conjecture
Bruno Pini Mathematical Analysis Seminar, 2016 We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic
Marco Mughetti
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Hypoellipticity in infinite dimensions and an application in interest rate theory [PDF]
, 2005 We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hormander's theorem for stochastic evolution equations in the spirit of Da Prato-Zabczyk. This result is used to show that HJM-equations from interest rate theory, which
Baudoin, Fabrice, Teichmann, Josef
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Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Abstract and Applied Analysis, 2013 General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties
Mawardi Bahri +2 more
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Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory [PDF]
, 2007 In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual $\LL(\Gc(\R^n),\wt{\C})$. After having proved the existence of a fundamental solution for a large class of partial differential operators ...
Garetto, Claudia
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