Related papers: Bounds on the state vector growth rate in stochast…
The mean growth rate of the state vector is evaluated for a generalized linear stochastic second-order system with a symmetric matrix. Diagonal entries of the matrix are assumed to be independent and exponentially distributed with different…
We consider stochastic discrete event dynamic systems that have time evolution represented with two-dimensional state vectors through a vector equation that is linear in terms of an idempotent semiring. The state transitions are governed by…
We consider generalized linear stochastic dynamical systems with second-order state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…
We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
We discuss the problem of counting the maximum number of distinct states that an isolated physical system can pass through in a given period of time---its maximum speed of dynamical evolution. Previous analyses have given bounds in terms of…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
In this paper, we examine the fundamental performance limitations in the control of stochastic dynamical systems; more specifically, we derive generic $\mathcal{L}_p$ bounds that hold for any causal (stabilizing) controllers and any…
The linear growth rate is commonly defined through a simple deterministic relation between the velocity divergence and the matter overdensity in the linear regime. We introduce a formalism that extends this to a nonlinear, stochastic…
We consider infinite particle system on the positive half-line moving independently of each other. When a particle hits the boundary it immediately disappears, and the boundary moves to the right on some fixed quantity (particle size). We…
Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for…
We develop precise bounds on the growth rates and fluctuation sizes of unbounded solutions of deterministic and stochastic nonlinear Volterra equations perturbed by external forces. The equation is sublinear for large values of the state,…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
Estimating the parameters governing the dynamics of a system is a prerequisite for its optimal control. We present a simple but powerful method that we call STEADY, for STochastic Estimation algorithm for DYnamical variables, to estimate…
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of…
When considering a general system of equations describing the space-time evolution (flow) of one or several variables, the problem of the optimization over a finite period of time of a measure of the state variable at the final time is a…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…