Related papers: Existence of L\'evy's area and pathwise integratio…

Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…

Let $\{X_{1}(t)\}_{0\leq t\leq1}$ and $\{X_{2}(t)\}_{0\leq t\leq1}$ be two independent continuous centered Gaussian processes with covariance functions$R_{1}$ and $R_{2}$. This paper shows that if the covariance functions are of finite…

The It\^o formula, also known as the change-of-variables formula, is a cornerstone of It\^o stochastic calculus. Over time, this formula has been extended to apply to random processes for which classical calculus is insufficient. Since…

Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…

Multi-vehicle coordinated decision making and control can improve traffic efficiency while guaranteeing driving safety. Formation control is a typical multi-vehicle coordination method in the multi-lane scenario. Among the existing…

We consider Malliavin calculus based on the It\^o chaos decomposition of square integrable random variables on the L\'evy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and…

We embed the rough integration in a larger geometrical/algebraic framework of integrating one-forms against group-valued paths, and reduce the rough integral to an inhomogeneous analogue of the classical Young integral. We define dominated…

We study a one-dimensional stochastic differential equation driven by a stable L\'evy process of order $\alpha$ with drift and diffusion coefficients $b,\sigma$. When $\alpha\in (1,2)$, we investigate pathwise uniqueness for this equation.…

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

This paper presents a simulation study on turnpike phenomena in stochastic optimal control problems. We employ the framework of Polynomial Chaos Expansions (PCE) to investigate the presence of turnpikes in stochastic LQ problems. Our…

We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the…

We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the…

We construct a new topology on the space of stopped paths and introduce a calculus for causal functionals on generic domains of this space. We propose a generic approach to pathwise integration without any assumption on the variation index…

Calibrating a L\'evy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and…

This article focuses on integrating path-planning and control with specializing on the unique needs of robotic unicycles. A unicycle design is presented which is capable of accelerating/breaking and carrying out a variety of maneuvers. The…

The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed…

This paper establishes a Transition Path Theory (TPT) for L\'{e}vy-type processes, addressing a critical gap in the study of the transition mechanism between meta-stabile states in non-Gaussian stochastic systems. A key contribution is the…

This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems. The approach is motivated by first showing that a lattice-based path planner can be…

In this work, we derive sufficient and necessary conditions for the existence of a weak and mild solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Levy process. Our approach requires to establish a…

We investigate pathwise turnpike behavior of discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process…