相关论文: Existence of L\'evy's area and pathwise integratio…

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…

We construct a pathwise integration theory, associated with a change of variable formula, for smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion of $p$-th variation along a sequence of time…

We provide a unified analytic approach to study stationary states of controlled differential equations driven by rough paths, using the framework of random dynamical systems and random attractors. Part I deals with driving paths of finite…

We investigate path-wise observables in experiments on driven colloids in a periodic light field to dissect selected intricate transport features, kinetics, and transition-path time statistics out of thermodynamic equilibrium. These…

We provide a simple algorithm for construction of Brownian paths approximating those of a L\'evy process on a finite time interval. It requires knowledge of the L\'evy process trajectory on a chosen regular grid and the law of its endpoint,…

We present a new version of the stochastic sewing lemma, capable of handling multiple discontinuous control functions. This is then used to develop a theory of rough stochastic analysis in a c\`adl\`ag setting. In particular, we define…

We consider controlling the paths of a spectrally negative L\'evy process by two means: the subtraction of `taxes' when the process is at an all-time maximum, and the addition of `bailouts' which keep the value of the process above zero. We…

We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…

We develop a stochastic integration theory for predictable integrands with respect to a L\'evy basis. Our approach is based on decoupling inequalities for tangent sequences and reduces the construction of the stochastic integral essentially…

Rough sheets are two-parameter analogs of rough paths. In this work the theory of integration over functions of two parameters is extended to cover the case of irregular functions by developing an appropriate notion of rough sheet. The main…

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property,…

We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure…

In this paper, we investigate the controllability of a class of formation control systems. Given a directed graph, we assign an agent to each of its vertices and let the edges of the graph describe the information flow in the system. We…

In line with the notion of probabilistic rough paths introduced in the previous contribution \cite{salkeld2021Probabilistic}, we address corresponding random controlled rough paths (first introduced in \cite{2019arXiv180205882.2B}), the…

We show that for $\gamma<\sqrt{4/3}$, it is possible to define the Levy area of a planar Brownian motion with the Liouville measure of intermittency parameter $\gamma$ as the underlying area measure. We also consider the case of smoother…

In this work, we introduce a theory of stochastic integration with respect to symmetric $\alpha$-stable cylindrical L\'evy processes. Since $\alpha$-stable cylindrical L\'evy processes do not enjoy a semi-martingale decomposition, our…

We investigate the properties of the path integral over reparametrizations (= the boundary value of the Liouville field in open string theory). Discretizing the path integral, we apply the Metropolis-Hastings algorithm to numerical…

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be…

Path integral control in Gaussian belief space requires a structural matching condition between the observation-driven diffusion of the belief mean and the actuation authority, which a fixed observation matrix cannot enforce. We treat the…

We develop the integration theory of two-parameter controlled paths $Y$ allowing us to define integrals of the form \begin{equation} \int_{[s,t] \times [u,v]} Y_{r,r'} \;d(X_{r}, X_{r'}) \end{equation} where $X$ is the geometric $p$-rough…