Related papers: Realizable monotonicity for continuous-time Markov…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…
In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…
In this paper, we are interested in investigating the perturbation bounds for the stationary distributions for discrete-time or continuous-time Markov chains on a countable state space. For discrete-time Markov chains, two new norm-wise…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
Spatial birth-and-death processes with a finite number of particles are obtained as unique solutions to certain stochastic equations. Conditions are given for existence and uniqueness of such solutions, as well as for continuous dependence…
Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics defining a…
We present a complexity measure for any finite time series. This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the…
Labeled continuous-time Markov chains (CTMCs) describe processes subject to random timing and partial observability. In applications such as runtime monitoring, we must incorporate past observations. The timing of these observations matters…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In…
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…
In this paper, we consider a type of time-changed Markov process, where the time-change is an inverse killed subordinator. This can be seen as an extension of Chen (Chen, Z., Time fractional equations and probabilistic representation, Chaos…
In this paper we consider a control problem for a Partially Observable Piecewise Deterministic Markov Process of the following type: After the jump of the process the controller receives a noisy signal about the state and the aim is to…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
We consider $k$-dimensional discrete-time systems of the form $x_{n+1}=F(x_n,\ldots,x_{n-k+1})$ in which the map $F$ is continuous and monotonic in each one of its arguments. We define a partial order on $\mathbb{R}^{2k}_+$, compatible with…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…