Related papers: On the dynamic programming principle for controlle…
Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…
The discrimination of quantum processes, including quantum states, channels, and superchannels, is a fundamental topic in quantum information theory. It is often of interest to analyze the optimal performance that can be achieved when…
The rates of activated processes, such as escape from a metastable state and nucleation, are exponentially sensitive to an externally applied field. We describe how this applies to modulation by high-frequency fields and illustrate it with…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The Pontryagin-type maximum principle derived in [30] for optimal control problems involving sweeping processes is generalized to the case where the sweeping set C is nonsmooth and not necessarily bounded, namely, C is the intersection of a…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…
In this short communication, we first recall a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. This result was recently obtained in [L. Bourdin and E. Tr{\'e}lat ,…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…
We propose a discretization of the optimality principle in dynamic programming based on radial basis functions and Shepard's moving least squares approximation method. We prove convergence of the approximate optimal value function to the…
The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not…
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward…
We study diffusion processes driven by a Brownian motion with regular drift in a finite dimension setting. The drift has two components on different time scales, a fast conservative component and a slow dissipative component. Using the…
This paper deals with unconstrained discounted continuous-time Markov decision processes in Borel state and action spaces. Under some conditions imposed on the primitives, allowing unbounded transition rates and unbounded (from both above…
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…
Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their…
This paper is concerned with the maximum principle and dynamic programming principle for mean-variance portfolio selection of jump diffusions and their relationship. First, the optimal portfolio and efficient frontier of the problem are…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…