Related papers: Bahadur--Kiefer Representations for Time Dependent…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the…
The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson…
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can…
In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on…
We conduct an empirical study using the quantile-based correlation function to uncover the temporal dependencies in financial time series. The study uses intraday data for the S\&P 500 stocks from the New York Stock Exchange. After…
The exact factorization of the time-dependent electron-nuclear wavefunction has been employed successfully in the field of quantum molecular dynamics simulations for interpreting and simulating light-induced ultrafast processes. In this…
In this article, we consider fractional derivatives of local time for $d-$dimensional centered Gaussian processes satisfying certain strong local nondeterminism property. We first give a condition for existence of fractional derivatives of…
We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-dependent generator of this exponential operator only depends…
Various recent results on quantum L\'evy processes are presented. The first part provides an introduction to the theory of L\'evy processes on involutive bialgebras. The notion of independence used for these processes is tensor…
We compute the Hamiltonian and Lagrangian associated to the large deviations of the trajectory of the empirical distribution for independent Markov processes, and of the empirical measure for translation invariant interacting Markov…
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on the…
We derive general results on the small deviation behavior for some classes of iterated processes. This allows us, in particular, to calculate the rate of the small deviations for $n$-iterated Brownian motions and, more generally, for the…
We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…
An $N$-dimensional nonlinear Fokker-Planck equation is investigated here by considering the time dependence of the coefficients, where drift-controlled and source terms are present. We exhibit the exact solution based on the generalized…
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
It is well known that Brownian motion enjoys several distributional invariances such as the scaling property and the time reversal. In this paper, we prove another invariance of Brownian motion that is compatible with the time reversal. The…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…