Related papers: Statistical determinism in non-Lipschitz dynamical…

Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…

We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…

This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of…

This work presents a new Distributionally Robust Optimization approach, using $p$-Wasserstein metrics, to analyze a stochastic program in a general context. The ambiguity set in this approach depends on the decision variable and is…

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…

In this paper, we introduce concepts of pathwise random almost periodic and almost automorphic solutions for dynamical systems generated by non-autonomous stochastic equations. These solutions are pathwise stochastic analogues of…

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for…

This survey paper is a structured concise summary of four of our recent papers on the stochastic regularity of diffusions that are associated to regular strongly local (but not necessarily symmetric) Dirichlet forms. Here by stochastic…

This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…

The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…

We study a class of stochastic differential equations with non-Lipschitzian coefficients.A unique strong solution is obtained and a large deviation principle of Freidln-Wentzell type has been established.

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…

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…

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…

The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…