Related papers: L^p estimates for Feynman-Kac propagators with tim…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
In this paper, we study the propagation speeds of reaction-diffusion-advection (RDA) fronts in time-periodic cellular and chaotic flows with Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We first apply the variational principle to…
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…
Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov…
This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
This paper investigates the transient probabilistic responses of nonlinear single-degree-of-freedom oscillators subjected to external fractional Gaussian noise (FGN) excitation. Owing to the inherent long-range correlations and memory…
Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…
Let $\nu$ be a positive measure on $[0,1]$. A Shimorin-type operator $T_\nu$ is an integral operator on the unit disk given by \[ T_\nu f(z) = \int_{\mathbb{D}} \frac{1}{1 - z\overline{\lambda}} \left( \int_0^1 \frac{d\nu(r)}{1 - r z…
In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…
In this manuscript, we provide a point-wise estimate for the $3$-commutators involving fractional powers of the sub-Laplacian on Carnot groups of homogeneous dimension $Q$. This can be seen as a fractional Leibniz rule in the sub-elliptic…
In this paper, we complete the study of mapping properties for a family of operators evaluating the difference between differentiation operators and conditional expectations acting on noncommutative $L_{p}$-spaces. To be more precise, we…
The fact that a Markov diffusion semi-group on $\mathbb R^d$ contracts the $L^p$ Wasserstein distance, which has been extensively used to establish uniform-in-time stability estimates (e.g. with respect to numerical discretization errors),…
We propose a method for computing the transfer entropy between time series using Ulam's approximation of the Perron-Frobenius (transfer) operator associated with the map generating the dynamics. Our method differs from standard transfer…
Let $\mathcal{M}$ be a semifinite von Neumann algebra equipped with a normal faithful semifinite trace $\tau$, and let $L_p(\mathcal{M})$ denote the associated noncommutative $L_p$-space for $1<p<\infty$. Let $n\in\mathbb{N}$ and let $a, b$…
We prove $L^{p}$ and weighted $L^{p}$ estimates for bounded functions of a selfadjoint operator satisfying both a pointwise gaussian estimate for its heat kernel and a finite speed of propagation property. As an application, we obtain…
We consider degenerate Kolmogorov-Fokker-Planck operators $$ \mathcal{L}u=\sum_{i,j=1}^{q}a_{ij}(x,t)\partial_{x_{i}x_{j}}^{2}u+\sum_{k,j=1}^{N}b_{jk}x_{k}\partial_{x_{j}}u-\partial_{t}u,\qquad (x,t)\in\mathbb{R}^{N+1},N\geq q\geq1 $$ such…
Many integrable stochastic particle systems in one space dimension (such as TASEP - Totally Asymmetric Simple Exclusion Process - and its $q$-deformation, the $q$-TASEP) remain integrable if we equip each particle with its own speed…
We establish the $L^p$-$L^q$-boundedness of subelliptic pseudo-differential operators on a compact Lie group $G$. Effectively, we deal with the $L^p$-$L^q$-bounds for operators in the sub-Riemmanian setting because the subelliptic classes…