Related papers: Similarity Between Two Stochastic Differential Sys…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
Decentralized optimization of distributed stochastic differential systems has been an active area of research for over half a century. Its formulation utilizing static team and person-by-person optimality criteria is well investigated.…
A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the…
Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and…
We propose a thermodynamically consistent minimal model to study synchronization which is made of driven and interacting three-state units. This system exhibits at the mean-field level two bifurcations separating three dynamical phases: a…
An equivalence is shown between a large class of deterministic dynamical systems and a class of stochastic processes, the balanced urn processes. These dynamical systems are governed by quasi-polynomial differential systems that are widely…
In this paper, we derive sufficient and necessary maximum principles for a stochastic optimal control problem where the system state is given by a controlled stochastic differential equation with default. We prove existence of a unique…
Reward fine-tuning of diffusion and flow models and sampling from tilted or Boltzmann distributions can both be formulated as stochastic optimal control (SOC) problems, where learning an optimal generative dynamics corresponds to optimizing…
We introduce an approach to inferring the causal architecture of stochastic dynamical systems that extends rate distortion theory to use causal shielding---a natural principle of learning. We study two distinct cases of causal inference:…
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
We introduce a notion of minimal uniform attractor for nonautonomous random dynamical systems, which depends jointly on time and on a random parameter. Several examples are provided to illustrate the concept and to compare it with existing…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
In stochastic optimal control, change of measure arguments have been crucial for stochastic analysis. Such an approach is often called static reduction in dynamic team theory (or decentralized stochastic control) and has been an effective…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…