相关论文: Discrete Capacity and Higher-order Differences of …

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition densities are proved. The observation time [0,T] may be fixed or lim n T = 0, where nh = T and h is a mesh…

This paper presents algorithms for identifying and reducing a dedicated set of controllable transition rates of a state-labelled continuous-time Markov chain model. The purpose of the reduction is to make states to satisfy a given…

Let $\{W_t\}_{t=1}^{\infty}$ be a finite state stationary Markov chain, and suppose that $f$ is a real-valued function on the state space. If $f$ is bounded, then Gillman's expander Chernoff bound (1993) provides concentration estimates for…

We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…

We derive a fine-grained uncertainty relation for the measurement of two incompatible observables on a single quantum system of continuous variables, and show that continuous variable systems are more uncertain than discrete variable…

This paper presents a convex optimization approach to control the density distribution of autonomous mobile agents with two control modes: ON and OFF. The main new characteristic distinguishing this model from standard Markov decision…

A fundamental problem when aggregating Markov chains is the specification of the number of state groups. Too few state groups may fail to sufficiently capture the pertinent dynamics of the original, high-order Markov chain. Too many state…

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain…

We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However,…

We study discrete-time, discrete-state multistate Markov models from the perspective of algebraic statistics. These models are widely studied in event history analysis, and are characterized by the state space, the initial distribution and…

We theoretically investigate and experimentally demonstrate the existence of topological edge states in a mechanical analog of the Kitaev chain with a non-zero chemical potential. Our system is a one-dimensional monomer system involving two…

Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a…

We show that the duality between channel capacity and data compression is retained when state information is available to the sender, to the receiver, to both, or to neither. We present a unified theory for eight special cases of channel…

Discrete time linear dynamical systems, including Markov chains, have found many applications including in security settings such as in cybersecurity operations center (CSOC) management and in managing health risks. However, in these two…

We consider the problem of steering control for the systems of one spin 1/2 particle and two interacting homonuclear spin 1/2 particles in an electro-magnetic field. The describing models are bilinear systems whose state varies on the Lie…

The problem of state communication over a discrete memoryless channel with discrete memoryless state is studied when the state information is available strictly causally at the encoder. It is shown that block Markov encoding, in which the…

We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular…