Sergio Albeverio
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Stochastic Quantization of the Three-Dimensional Polymer Measure via Dirichlet Form Method Open
We prove that there exists a diffusion process whose invariant measure is the three-dimensional polymer measure $$\nu _\lambda $$ for all $$\lambda >0$$ . We follow in part a previous incomplete unpublished work of the first named…
Semigroups on generalized Sobolev spaces associated with Laplacians with applications Stochastic PDEs with singular boundary conditions Open
Laplacians associated with domains with singular boundary conditions and are considered together with semigroups on generalized Sobolev spaces, they generate. Applications are given to stochastic PDEs with singular boundary conditions.
Stochastic quantization of the three-dimensional polymer measure via the Dirichlet form method Open
We prove that there exists a diffusion process whose invariant measure is the three dimensional polymer measure $ν_λ$ for all $λ>0$. We follow in part a previous incomplete unpublished work of the first named author with M. Röckner and X.Y…
A general formulation of Non-Local Dirichlet forms on infinite dimensional topological vector spaces and its applications, and corresponding subjects: Seminar at Univ. Lisboa,2023 Open
A concise explanations on the results given by Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces I, CMP 2021, by Sergio Albeverio, Minoru W. Yoshida, et.al., and Non-local Markovian Symmetric Forms on Infinite Dimensional …
High accuracy distinction of shockable and non-shockable arrhythmias in abnormal classes through wavelet transform with pseudo differential like operators Open
Arrhythmia is an abnormal rhythm of the heart which leads to sudden death. Among these arrhythmias, some are shockable, and some are non-shockable arrhythmias with external defibrillation. The automated external defibrillator (AED) is used…
On the construction and identification of Boltzmann processes Open
Given the existence of a solution {f (t, x, z)} t≥0 of the Boltzmann equation for hard spheres, we introduce a stochastic differential equation driven by a Poisson random measure that depends on the densities {f (t, x, z)} t≥0 .The margina…
Singular perturbations and asymptotic expansions for SPDEs with an application to term structure models Open
We study the dependence of mild solutions to linear stochastic evolution equations on Hilbert space driven by Wiener noise, with drift having linear part of the type A+εG, on the parameter ε. In particular, we study the limit and the asymp…
Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces Open
The general framework on the non-local Markovian symmetric forms on weighted l p $(p \in [1, \infty ])$ spaces constructed by Albeverio et al. (Commn. Math. Phys. 388 , 659–706, 2021 Kagawa) by restricting the situation where p =…
Optimal bounds on the speed of subspace evolution* Open
By a quantum speed limit one usually understands an estimate on how fast a quantum system can evolve between two distinguishable states. The most known quantum speed limit is given in the form of the celebrated Mandelstam–Tamm inequality t…
Quantum Speed Limits for Time Evolution of a System Subspace Open
One of the fundamental physical limits on the speed of time evolution of a quantum state is known in the form of the celebrated Mandelstam-Tamm inequality. This inequality gives an answer to the question on how fast an isolated quantum sys…
View article: Mean-Field Limit for a Class of Stochastic Ergodic Control Problems
Mean-Field Limit for a Class of Stochastic Ergodic Control Problems Open
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 23 October 2020Accepted: 18 October 2021Published online: 14 February 2022Keywordsmean-field control, ergodic opti…
Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces I. The closability and quasi-regularity Open
General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces $$(S, \mathcal{B}(S), \mu )$$ , with S Fréchet spaces such that $$S \subset {{\mathbb {R}}}^{{\mathbb {N}}}$$…
Non-local Markovian symmetric forms on infinite dimensional spaces; Part 2. Examples: non local stochastic quantization of space cut-off quantum fields and infinite particle systems Open
The general framework on the non-local Markovian symmetric forms on weighted $l^p$ $(p \in [1, \infty])$ spaces constructed by [A,Kagawa,Yahagi,Y 2020], by restricting the situation where $p =2$, is applied to such measure spaces as the sp…
Construction of a non-Gaussian and rotation-invariant $\Phi ^4$-measure and associated flow on ${\mathbb R}^3$ through stochastic quantization Open
A new construction of non-Gaussian, rotation-invariant and reflection positive probability measures $\mu$ associated with the $\varphi ^4_3$-model of quantum field theory is presented. Our construction uses a combination of semigroup metho…
Construction of a non-Gaussian and rotation-invariant $Φ^4$-measure and associated flow on ${\mathbb R}^3$ through stochastic quantization Open
A new construction of non-Gaussian, rotation-invariant and reflection positive probability measures $μ$ associated with the $φ^4_3$-model of quantum field theory is presented. Our construction uses a combination of semigroup methods, and m…
View article: Random transformations and invariance of semimartingales on Lie groups
Random transformations and invariance of semimartingales on Lie groups Open
Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian motion. A necessary and sufficient explicit condition character…
On the Hausdorff dimension faithfulness and the Cantor series expansion Open
We study families $Φ$ of coverings which are faithful for the Hausdorff dimension calculation on a given set $E$ (i. e., special relatively narrow families of coverings leading to the classical Hausdorff dimension of an arbitrary subset of…
Singular perturbations and asymptotic expansions for SPDEs with an application to term structure models Open
We study the dependence of mild solutions to linear stochastic evolution equations on Hilbert space driven by Wiener noise, with drift having linear part of the type $A+\varepsilon G$, on the parameter $\varepsilon$. In particular, we stud…
Non-local Markovian symmetric forms on infinite dimensional spaces Open
General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces $(S, {\cal B}(S), μ)$, with $S$ Fr{é}chet spaces such that $S \subset {\mathbb R}^{\mathbb N}$, ${\cal B}(S)$ is the Bore…
View article: Grassmannian stochastic analysis and the stochastic quantization of Euclidean Fermions
Grassmannian stochastic analysis and the stochastic quantization of Euclidean Fermions Open
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum pro…
View article: Mean-field limit for a class of stochastic ergodic control problems
Mean-field limit for a class of stochastic ergodic control problems Open
We study a family of McKean-Vlasov (mean-field) type ergodic optimal control problems with linear control, and quadratic dependence on control of the cost function. For this class of problems we establish existence and uniqueness of an opt…
The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity Open
In this note we consider a quantum mechanical particle moving inside an\ninfinitesimally thin layer constrained by a parabolic well in the $x$-direction\nand, moreover, in the presence of an impurity modelled by an attractive\nGaussian pot…