Related papers: Stochastic Calculus as Operator Factorization An O…

In this paper we present a factorization framework for Hermite subdivision schemes refining function values and first derivatives, which satisfy a spectral condition of high order. In particular we show that spectral order $d$ allows for…

We show that the expected solution operator of prototypical linear elliptic partial differential operators with random coefficients is well approximated by a computable sparse matrix. This result is based on a random localized orthogonal…

In this paper we work with the approximation of unitary groups of operators of the form $e^{-itH}$ where $H\in\mathscr{L}(\mathcal{H})$ is the Hamiltonian of a given quantum dynamical system modeled in the discretizable Hilbert space…

With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…

As a new technique it is shown how general pseudo-differential operators can be estimated at arbitrary points in Euclidean space when acting on functions $u$ with compact spectra. The estimate is a factorisation inequality, in which one…

In this work we extend the Kugo-Ojima-Nakanishi covariant operator formalism to quantize two higher derivative systems, considering their extended phase space structures. More specifically, the one describing spin-$0$ particles by a vector…

In this paper we study the approximation of the distribution of $X_t$ Hilbert--valued stochastic process solution of a linear parabolic stochastic partial differential equation written in an abstract form as $$ dX_t+AX_t dt = Q^{1/2} d W_t,…

We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of a maximal monotone operator and a single-valued maximal monotone cocoercive operator. This…

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

When ${\cal{D}}: E \rightarrow F$ is a linear differential operator of order $q$ between the sections of vector bundles over a manifold $X$ of dimension $n$, it is defined by a bundle map $\Phi: J_q(E) \rightarrow F=F_0$ that may depend,…

We present an algorithm for factoring linear differential operators with coefficients in a finite separable extension of F p (x). Our methods rely on specific tools arising in positive characteristic: p-curvature, structure of simple…

This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…

A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative…

We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the…

We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…

Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…

For any unitary representation $\rho$ on a finite-dimensional Hilbert space \(V\) with differential \(d\rho : \mathfrak{g} \to \mathfrak{u}(V)\) for the Lie algebra $\mathfrak g$, we consider the Hamiltonian evolution \[ U_X(t) \coloneqq…

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…

In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…

The standard oracle operator corresponding to a function f is a unitary operator that computes this function coherently, i.e. it maintains superpositions. This operator acts on a bipartite system, where the subsystems are the input and…