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ORBi

Publications DMATH
Invariant density adaptive estimation for ergodic jump diffusion processes over anisotropic classes Amorino, Chiara ; in Journal of Statistical Planning and Inference (in press) We consider the solution of a multivariate stochastic differential equation with Levy-type jumps and with unique invariant probability measure with density μ. We assume that a continuous record of ... [more ▼] We consider the solution of a multivariate stochastic differential equation with Levy-type jumps and with unique invariant probability measure with density μ. We assume that a continuous record of observations is available. In the case without jumps, Reiss and Dalalyan [7] and Strauch [24] have found convergence rates of invariant density estimators, under respectively isotropic and anisotropic H ̈older smoothness constraints, which are considerably faster than those known from standard multivariate density estimation. We extend the previous works by obtaining, in presence of jumps, some estimators which have the same convergence rates they had in the case without jumps for d ≥ 2 and a rate which depends on the degree of the jumps in the one-dimensional setting. We propose moreover a data driven bandwidth selection procedure based on the Goldenshluger and Lepski method [11] which leads us to an adaptive non-parametric kernel estimator of the stationary density μ of the jump diffusion X. [less ▲] Detailed reference viewed: 95 (17 UL)Semiparametric estimation of McKean-Vlasov SDEs ; Pilipauskaite, Vytauté ; Podolskij, Mark in Annales de l'Institut Henri Poincaré (B), Probabilités et Statistiques (in press) Detailed reference viewed: 231 (12 UL)The mod 2 cohomology rings of congruence subgroups in the Bianchi groups ; ; Rahm, Alexander E-print/Working paper (in press) We provide new tools for the calculation of the torsion in the cohomology of congruence subgroups in the Bianchi groups : An algorithm for finding particularly useful fundamental domains, and an analysis ... [more ▼] We provide new tools for the calculation of the torsion in the cohomology of congruence subgroups in the Bianchi groups : An algorithm for finding particularly useful fundamental domains, and an analysis of the equivariant spectral sequence combined with torsion subcomplex reduction. [less ▲] Detailed reference viewed: 340 (25 UL)Multivariate stable approximation in Wasserstein distance by Stein's method ; Nourdin, Ivan ; et al in Journal of Theoretical Probability (in press) Detailed reference viewed: 97 (4 UL)Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows ; Thalmaier, Anton in Analysis and PDE (in press) Let M be a differentiable manifold endowed with a family of complete Riemannian metrics g(t) evolving under a geometric flow over the time interval [0,T[. In this article, we give a probabilistic ... [more ▼] Let M be a differentiable manifold endowed with a family of complete Riemannian metrics g(t) evolving under a geometric flow over the time interval [0,T[. In this article, we give a probabilistic representation for the derivative of the corresponding conjugate semigroup on M which is generated by a Schrödinger type operator. With the help of this derivative formula, we derive fundamental Harnack type inequalities in the setting of evolving Riemannian manifolds. In particular, we establish a dimension-free Harnack inequality and show how it can be used to achieve heat kernel upper bounds in the setting of moving metrics. Moreover, by means of the supercontractivity of the conjugate semigroup, we obtain a family of canonical log-Sobolev inequalities. We discuss and apply these results both in the case of the so-called modified Ricci flow and in the case of general geometric flows. [less ▲] Detailed reference viewed: 140 (13 UL)Generating Picard modular forms by invariant theory ; van der Geer, Gerard in Pure and Applied Mathematics Quarterly (in press) Detailed reference viewed: 29 (0 UL)Invariance in a class of operations related to weighted quasi-geometric means Devillet, Jimmy ; in Fuzzy Sets and Systems (in press) Let $I\subset (0,\infty )$ be an interval that is closed with respect to the multiplication. The operations $C_{f,g}\colon I^{2}\rightarrow I$ of the form \begin{equation*} C_{f,g}\left( x,y\right) =\left ... [more ▼] Let $I\subset (0,\infty )$ be an interval that is closed with respect to the multiplication. The operations $C_{f,g}\colon I^{2}\rightarrow I$ of the form \begin{equation*} C_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\left( x\right) \cdot g\left( y\right) \right) \text{,} \end{equation*} where $f,g$ are bijections of $I$ are considered. Their connections with generalized weighted quasi-geometric means is presented. It is shown that invariance\ question within the class of this operations leads to means of iterative type and to a problem on a composite functional equation. An application of the invariance identity to determine effectively the limit of the sequence of iterates of some generalized quasi-geometric mean-type mapping, and the form of all continuous functions which are invariant with respect to this mapping are given. The equality of two considered operations is also discussed. [less ▲] Detailed reference viewed: 96 (7 UL)Margulis Multiverse: Infinitesimal Rigidity, Pressure Form and Convexity Ghosh, Sourav in Transactions of the American Mathematical Society (in press) Detailed reference viewed: 45 (0 UL)Multiple Sets Exponential Concentration and Higher Order Eigenvalues ; Herry, Ronan in Potential Analysis (in press) On a generic metric measured space, we introduce a notion of improved concentration of measure that takes into account the parallel enlargement of k distinct sets. We show that the k-th eigenvalues of the ... [more ▼] On a generic metric measured space, we introduce a notion of improved concentration of measure that takes into account the parallel enlargement of k distinct sets. We show that the k-th eigenvalues of the metric Laplacian gives exponential improved concentration with k sets. On compact Riemannian manifolds, this allows us to recover estimates on the eigenvalues of the Laplace-Beltrami operator in the spirit of an inequality of Chung, Grigor’yan & Yau, Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Adv. Math. 117(2), 165–178 (1996). [less ▲] Detailed reference viewed: 137 (6 UL)Rubik's Snakes on a plane Grotto, Francesco ; Perucca, Antonella ; in College Mathematics Journal (in press) Detailed reference viewed: 166 (38 UL)Characterization of field homomorphisms through Pexiderized functional equations ; Kiss, Gergely ; in Journal of Difference Equations and Applications (in press) Detailed reference viewed: 101 (6 UL)Limit theorems for additive functionals of the fractional Brownian motion ; Nourdin, Ivan ; et al in Annals of Probability (in press) Detailed reference viewed: 90 (16 UL)Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance Kasprzak, Mikolaj ; Peccati, Giovanni in Annals of Applied Probability (in press) Detailed reference viewed: 30 (1 UL)Splitting fields of X^n-X-1 (particularly for n=5), prime decomposition and modular forms ; La Rosa, Alfio Fabio ; Wiese, Gabor in Expositiones Mathematica (in press) We study the splitting fields of the family of polynomials $f_n(X)= X^n-X-1$. This family of polynomials has been much studied in the literature and has some remarkable properties. Serre related the ... [more ▼] We study the splitting fields of the family of polynomials $f_n(X)= X^n-X-1$. This family of polynomials has been much studied in the literature and has some remarkable properties. Serre related the function on primes $N_p(f_n)$, for a fixed $n \leq 4$ and $p$ a varying prime, which counts the number of roots of $f_n(X)$ in $\mathbb F_p$ to coefficients of modular forms. We study the case $n=5$, and relate $N_p(f_5)$ to mod $5$ modular forms over $\mathbb Q$, and to characteristic 0, parallel weight 1 Hilbert modular forms over $\mathbb Q(\sqrt{19 \cdot 151})$. [less ▲] Detailed reference viewed: 87 (7 UL)Visual characterization of associative quasitrivial nondecreasing functions on finite chains Kiss, Gergely in Fuzzy Sets and Systems (in press) Detailed reference viewed: 66 (8 UL)Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees ; Peccati, Giovanni ; in Random Structures and Algorithms (in press) Detailed reference viewed: 74 (6 UL)Maximal and Typical topology of real polynomial singularities ; Stecconi, Michele in Annales de l'Institut Fourier (in press) Detailed reference viewed: 28 (0 UL)A generalization of Bohr-Mollerup's theorem for higher order convex functions: A tutorial Marichal, Jean-Luc ; in Aequationes Mathematicae (in press) In its additive version, Bohr-Mollerup's remarkable theorem states that the unique (up to an additive constant) convex solution $f(x)$ to the equation $\Delta f(x)=\ln x$ on the open half-line $(0,\infty ... [more ▼] In its additive version, Bohr-Mollerup's remarkable theorem states that the unique (up to an additive constant) convex solution $f(x)$ to the equation $\Delta f(x)=\ln x$ on the open half-line $(0,\infty)$ is the log-gamma function $f(x)=\ln\Gamma(x)$, where $\Delta$ denotes the classical difference operator and $\Gamma(x)$ denotes the Euler gamma function. In a recently published open access book, the authors provided and illustrated a far-reaching generalization of Bohr-Mollerup's theorem by considering the functional equation $\Delta f(x)=g(x)$, where $g$ can be chosen from a wide and rich class of functions that have convexity or concavity properties of any order. They also showed that the solutions $f(x)$ arising from this generalization satisfy counterparts of many properties of the log-gamma function (or equivalently, the gamma function), including analogues of Bohr-Mollerup's theorem itself, Burnside's formula, Euler's infinite product, Euler's reflection formula, Gauss' limit, Gauss' multiplication formula, Gautschi's inequality, Legendre's duplication formula, Raabe's formula, Stirling's formula, Wallis's product formula, Weierstrass' infinite product, and Wendel's inequality for the gamma function. In this paper, we review the main results of this new and intriguing theory and provide an illustrative application. [less ▲] Detailed reference viewed: 88 (14 UL)On deformation quantization of quadratic Poisson structures Merkoulov (merkulov), Serguei ; in Communications in Mathematical Physics (in press) We study the deformation complex of the dg wheeled properad of Z-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application ... [more ▼] We study the deformation complex of the dg wheeled properad of Z-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the Grothendieck-Teichmüller group acts on the genus completion of that wheeled properad faithfully and essentially transitively. As a second application we classify all universal quantizations of Z-graded quadratic Poisson structures together with the underlying (so called) homogeneous formality maps. [less ▲] Detailed reference viewed: 106 (3 UL)Kummer theory for products of one-dimensional tori Perissinotto, Flavio ; Perucca, Antonella in Publications Mathematiques de Besançon (in press) Let T be a finite product of one-dimensional tori defined over a number field K. We consider the torsion-Kummer extension K(T[nt], (1/n)G), where n,t are positive integers and G is a finitely generated ... [more ▼] Let T be a finite product of one-dimensional tori defined over a number field K. We consider the torsion-Kummer extension K(T[nt], (1/n)G), where n,t are positive integers and G is a finitely generated group of K-points on T. We show how to compute the degree of K(T[nt], (1/n)G) over K and how to determine whether T is split over such an extension. If K=Q, then we may compute at once the degree of the above extensions for all n and t. [less ▲] Detailed reference viewed: 174 (44 UL) |
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