Related papers: Quadratic harnesses from generalized beta integral…
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…
We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-commutation relation. This implies that quadratic harnesses are…
We introduce polynomial processes taking values in an arbitrary Banach space $B$ via their infinitesimal generator $L$ and the associated martingale problem. We obtain two representations of the (conditional) moments in terms of solutions…
In this paper we deal with the generalized Gamma processes and their compositions. For the compositions of two or more than two generalized Gamma processes we give, when possible, the explicit law whereas, in the other cases the…
Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to…
According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
Mat\'ern's hard-core processes are valuable point process models in spatial statistics. In order to extend their field of application, Mat\'ern's original models are generalized here, both as point processes and particle processes. The…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Iteration of randomly chosen quadratic maps defines a Markov process: X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with values in the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta x(1-x). Its study is of…
A Generalised Hadamard Transform for multi-phase or multilevel signals is introduced, which includes the Fourier, Generalised, Discrete Fourier, Walsh-Hadamard and Reverse Jacket Transforms. The jacket construction is formalised and shown…
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…
We introduce a Bayesian framework for inference with a supervised version of the Gaussian process latent variable model. The framework overcomes the high correlations between latent variables and hyperparameters by using an unbiased pseudo…
Banded matrices can be used as precision matrices in several models including linear state-space models, some Gaussian processes, and Gaussian Markov random fields. The aim of the paper is to make modern inference methods (such as…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
We construct manifold structures on various sets of solutions of the general relativistic initial data sets.
The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
The generalized Langevin equation is used as a model for various coarse-grained physical processes, e.g., the time evolution of the velocity of a given larger particle in an implicitly represented solvent, when the relevant time scales of…