相关论文: Systems with distributions and viability theorem
We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
General distribution steering is intrinsically an infinite-dimensional problem, when the continuous distributions to steer are arbitrary. We put forward a moment representation of the primal system for control in [42]. However, the system…
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the…
This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional It\^{o} diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ can be…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
We investigate the limit-point/limit-circle classification for the differential equation $Ju'+qu=\lambda wu$ where $J=\big(\begin{smallmatrix}0&-1\\ 1&0\end{smallmatrix}\big)$ and $q$ and $w$ are matrices whose entries are distributions of…
In this paper we will study integrability of distributions whose primitives are left regulated functions and locally or globally integrable in the Henstock--Kurzweil, Lebesgue or Riemann sense. Corresponding spaces of distributions and…
In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
We revisit the fundamental problem of learning with distribution shift, in which a learner is given labeled samples from training distribution $D$, unlabeled samples from test distribution $D'$ and is asked to output a classifier with low…
The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could…
In this paper we focus on regional deterministic optimal control problems, i.e., problems where the dynamics and the cost functional may be different in several regions of the state space and present discontinuities at their interface.…