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Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime…

It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type…

We introduce a stochastic principal-agent model. A principal and an agent interact in a stochastic environment, each privy to observations about the state not available to the other. The principal has the power of commitment, both to elicit…

This paper studies the performative prediction problem which optimizes a stochastic loss function with data distribution that depends on the decision variable. We consider a setting where the agent(s) provides samples adapted to the…

This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…

This paper introduces a novel motion planning algorithm for stochastic scenarios. We extend the concept of a navigation function to such scenarios. Our main idea is to consider both the Gaussian distribution probabilities of the players'…

We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…

We investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of stochastic differential equations describing a prey-predator model perturbed by Gaussian noise. We first establish, for any fixed…

We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…

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…

Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…

Distribution shifts have long been regarded as troublesome external forces that a decision-maker should either counteract or conform to. An intriguing feedback phenomenon termed decision dependence arises when the deployed decision affects…

In this paper, we investigate how to achieve the unpredictability against malicious inferences for linear systems. The key idea is to add stochastic control inputs, named as unpredictable control, to make the outputs irregular. The future…

The socioeconomic impact of pollution naturally comes with uncertainty due to, e.g., current new technological developments in emissions' abatement or demographic changes. On top of that, the trend of the future costs of the environmental…

We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…

Nontransitive choices have long been an area of curiosity within economics. However, determining whether nontransitive choices represent an individual's preference is a difficult task since choice data is inherently stochastic. This paper…

We consider a general class of dynamic resource allocation problems within a stochastic optimal control framework. This class of problems arises in a wide variety of applications, each of which intrinsically involves resources of different…

Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…

We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…

Stochastic systems are used to model a variety of phenomena in which noise plays an essential role. In these models, one potential goal is to determine if noise can induce transitions between states, and if so, to calculate the most…