Related papers: Generalized Fock space and moments
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
The definition of generalized random processes in Gel'fand sense allows to extend well-known stochastic models, such as the fractional Brownian motion, and study the related fractional pde's, as well as stochastic differential equations in…
A study on the notion of covariant derivatives in flat and curved space-time via It\^o-Wiener processes, when subjected to stochastic processes, is presented. Going into details, there is an analysis of the following topics: (i) Besov…
For a general class of Gaussian processes $W$, indexed by a sigma-algebra $\mathscr F$ of a general measure space $(M,\mathscr F, \sigma)$, we give necessary and sufficient conditions for the validity of a quadratic variation representation…
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of…
In this article we give an introduction to the Fock quantization of the Maxwell field. At the classical level, we treat the theory in both the covariant and canonical phase space formalisms. The approach is general since we consider…
The aim of this work is to define and perform a study of local times of all Gaussian processes that have an integral representation over a real interval (that maybe infinite). Very rich, this class of Gaussian processes, contains Volterra…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
Upon its inception the theory of regularity structures allowed for the treatment for many semilinear perturbations of the stochastic heat equation driven by space-time white noise. When the driving noise is non-Gaussian the machinery of…
On a closed Riemannian manifold, we construct a family of intrinsic Gaussian noises indexed by a regularity parameter $\alpha\geq0$ to study the well-posedness of the parabolic Anderson model. We show that with rough initial conditions, the…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
We extend the It\^o-Wentzell formula for the evolution along a continuous semimartingale of a time-dependent stochastic field driven by a continuous semimartingale to tensor field-valued stochastic processes on manifolds. More concretely,…
In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in $\mathbb{R}^d$ with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the…
We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements. Our method simultaneously learns a continuous time model and a scalar energy function…
We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…
We consider a generalized method of moments framework in which a part of the data vector is missing for some units in a completely unrestricted, potentially endogenous way. In this setup, the parameters of interest are usually only…
We develop the general formalism for the study of neutrino propagation in presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher…