Related papers: Stochastic Variational formulas for solutions to l…

We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton…

We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the…

The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…

Guidance is a cornerstone of modern diffusion models, playing a pivotal role in conditional generation and enhancing the quality of unconditional samples. However, current approaches to guidance scheduling--determining the appropriate…

This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…

This paper is addressed to studying the exact controllability for stochastic transport equations by two controls: one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term. By…

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…

We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…

This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yield deterministic as well as stochastic constrained…

A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…

We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…

Although the mean-variance control was initially formulated for financial portfolio management problems in which one wants to maximize expected return and control the risk, our motivations also stem from highway vehicle platoon controls…

A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.

We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…

In this paper, we solve an open problem and obtain a general maximum principle for a stochastic optimal control problem where the control domain is an arbitrary non-empty set and all the coefficients (especially the diffusion term and the…

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…

This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between…

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…

In this article, we study the classical finite-horizon optimal stopping problem for multidimensional diffusions through an approach that differs from what is typically found in the literature. More specifically, we first prove a key…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…