Related papers: Simulating non-Markovian stochastic processes
We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and…
Non-Markovianity, the intricate dependence of an open quantum system on its temporal evolution history, holds tremendous implications across various scientific disciplines. However, accurately characterizing the complex non-Markovian…
We analyze a non-Markovian mean field interacting spin system, related to the Curie--Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…
The understanding of memory effects arising from the interaction between system and environment is a key for engineering quantum thermodynamic devices beyond the standard Markovian limit. We study the performance of measurement-based…
The simulation of quantum processes is a key goal for the grand programme aiming at grounding quantum technologies as the way to explore complex phenomena that are inaccessible through standard, classical calculators. Some interesting steps…
Although Gillespie's algorithm is justified under a set of axioms based on the assumption of homogeneity of the system, many chemical systems deviate from this assumption, as is the case for reactions taking place in low-mobility media.…
Many biological, social and man-made systems are better described in terms of temporal networks, i.e. networks whose links are only present at certain points in time, rather than by static ones. In particular, it has been found that…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
In this paper we apply a methodology introduced in Navarro Jimenez et al (2016) in the framework of chemical reaction networks to perform a global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by…
Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
At the fundamental conceptual level, two alternatives have traditionally been considered for how mutations arise and how evolution happens: 1) random mutation and natural selection, and 2) Lamarckism. Recently, the theory of…
In this paper we introduce and analyze a class of diffusion type equations related to certain non-Markovian stochastic processes. We start from the forward drift equation which is made non-local in time by the introduction of a suitable…
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
We propose a method for the algorithmic quantum simulation of memory effects described by integrodifferential evolution equations. It consists in the systematic use of perturbation theory techniques and a Markovian quantum simulator. Our…