相关论文: Remarks on invariance of population distributions …
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
We define a Markov process on the set of countable graphs with spins. Transitions are local substitutions in the graph. It is proved that the scaling macrodimension is an invariant of such dynamics.
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…
We study in this paper certain properties of the responses of dynamical systems to external inputs. The motivation arises from molecular systems biology. and, in particular, the recent discovery of an important transient property, related…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
The dynamics of the solutions to a class of conservative SPDEs are analysed from two perspectives: Firstly, a probabilistic construction of a corresponding random dynamical system is given for the first time. Secondly, the existence and…
Consider a continuous time particle system $\eta^t=(\eta^t(k),k\in \mathbb{L})$, indexed by a lattice $\mathbb{L}$ which will be either $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, a segment $\{1,\cdots, n\}$, or $\mathbb{Z}^d$, and taking its…
Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behaviour and for its possible application in near-term quantum technologies. However, understanding these…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total…
The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…
We consider a Markovian evolution on point processes, the $\Psi$--process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a…
We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the…