Related papers: Functional integral approach for multiplicative st…
Path dependence is omnipresent in many disciplines such as engineering, system theory and finance. It reflects the influence of the past on the future, often expressed through functionals. However, non-Markovian problems are often…
The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighborhood of a given saddlepoint exactly by means of a smooth…
Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic…
This paper presents a direct method to obtain the deterministic and stochastic contribution of the sum of two independent sets of stochastic processes, one of which is composed by Ornstein-Uhlenbeck processes and the other being a general…
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse…
Multiplicative white-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its…
Fourier-Wiener transform of the formal expression for multiple self-intersection local time is described in terms of the integral, which is divergent on the diagonals. The method of regularization we use in this work related to…
In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space $\Phi$. Our construction of the stochastic integral is based on the theory of tensor products…
The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…
Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a…
It is well known that perturbative solutions of the Langevin equation can be used to calculate correlation functions in stochastic quantization. However, this work is challenging due to the absence of generalized rules. In this paper, we…
We apply the operator approach to a stochastic system belonging to a class of death-birth processes, which we introduce utilizing the master equation approach. By employing Doi- Peliti formalism we recast the master equation in the form of…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow one…
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate…
We provide explicit series expansions to certain stochastic path-dependent integral equations in terms of the path signature of the time augmented driving Brownian motion. Our framework encompasses a large class of stochastic linear…
We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian functions and of multiple products of Hermite polynomials.
Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas…