Related papers: Rough path theory and an introduction to rough par…
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…
The aim of this textbook is to provide students with basic knowledge of stochastic models that may apply to telecommunications research areas, such as traffic modelling, resource provisioning and traffic management. These study areas are…
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
We go ahead with the study initiated in [3] about a heat-equation model with non-linear perturbation driven by a space-time fractional noise. Using general results from Hairer's theory of regularity structures, the analysis reduces to the…
Stochastic differential equations (SDEs) on compact foliated spaces were introduced a few years ago. As a corollary, a leafwise Brownian motion on a compact foliated space was obtained as a solution to an SDE. In this paper we construct…
In this research a new algebraic semantics of rough set theory including additional meta aspects is proposed. The semantics is based on enhancing the standard rough set theory with notions of 'relative ability of subsets of approximation…
In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…
We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory allowing to handle generalized integrals weighted by an exponential coefficient. The results are applied to the fractional…
In this Note, we study a transport-diffusion equation with rough coefficients and we prove that solutions are unique in a low-regularity class.
We investigate path integral formalism for continuum theory. It is shown that the path integral for the soft modes can be represented in the form of a lattice theory. Kinetic term of this lattice theory has a standard form and potential…
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
Rough stochastic differential equations (RSDEs) are common generalisations of Ito SDEs and Lyons RDEs and have emerged as new tool in several areas of applied probability, including non-linear stochastic filtering, pathwise stochastic…
We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly.…
We build a connection between rough path theory and noncommutative algebra, and interpret the integration of geometric rough paths as an example of a non-abelian Young integration. We identify a class of slowly-varying one-forms, and prove…
An informal introduction to some new geometric partial differential equations motivated by string theories is provided. Some of these equations are also interesting from the point of view of non-K\"ahler geometry and the theory of…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…
Since the breakthrough in rough paths theory for stochastic ordinary differential equations (SDEs), there has been a strong interest in investigating the rough differential equation (RDE) approach and its numerous applications. Rough path…