Related papers: Similarity Between Two Stochastic Differential Sys…
Stochastic hybrid systems are dynamic systems that undergo both random continuous-time flows and random discrete jumps. Depending on how randomness is introduced into the continuous dynamics, discrete transitions, or both, stochastic hybrid…
In this paper we propose a compositional framework for the construction of approximations of the interconnection of a class of stochastic hybrid systems. As special cases, this class of systems includes both jump linear stochastic systems…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given…
Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…
We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic…
In this paper we develop a new tool for the comparison of paired data based on a new criterion of stochastic dominance that takes into account the dependence structure of the random variables under comparison. This new procedure provides a…
Computationally efficient solutions for pseudometrics quantifying deviation from topological conjugacy between dynamical systems are presented. Deviation from conjugacy is quantified in a Pareto optimal sense that accounts for spectral…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
H. Lin and the author introduced the notion of approximate conjugacy of dynamical systems. In this paper, we will discuss the relationship between approximate conjugacy and full groups of Cantor minimal systems. An analogue of…
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
We investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…
Conformance is defined as a measure of distance between the behaviors of two dynamical systems. The notion of conformance can accelerate system design when models of varying fidelities are available on which analysis and control design can…