Related papers: Evolutionary semigroups on path spaces
A survey of the probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. The relations with the…
We consider a stationary Markovian evolution with values on a disjointly partitioned set space $I\sqcup {\cal E}$. The evolution is visible (in the sense of knowing the transition probabilities) on the states in $I$ but not for the states…
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
We review the theory of one-sided coupled operator matrices with a focus on evolution equations with inhomogeneous boundary conditions. (The original article had no abstract.)
We consider a class of space-time coupled evolution equations (CEEs), obtained by a subordination of the heat operator. Our CEEs reformulate and extend known governing equations of non-Markovian processes arising as scaling limits of…
A 3D stochastic Navier-Stokes equation with a suitable non degenerate additive noise is considered. The regularity in the initial conditions of every Markov transition kernel associated to the equation is studied by a simple direct…
In this paper, we employ Markov process theory to prove asymptotic results for a class of stochastic processes which arise as solutions of a stochastic evolution inclusion and are given by the representation formula \begin{align*}…
Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…
We characterize Markov lattice semigroups induced by measurable semiflows on probability spaces by properties of their generators. In addition we construct topological models on compact spaces for such semigroups.
We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space R^d. In particular Markov processes related to sub-Markovian kernels, but also non-Markovian processes…
Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates.…
Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on real separable Hilbert space whose…
We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the…
We provide an introduction to deformation quantisation and discuss the application of the formalism in solving the evolution problem for many-body systems in terms of semiclassical expansion. In any fixed order of expansion over the…
We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time…
The classical notion of L\'evy process is generalized to one that takes as its values probabilities on a first order model equipped with a commutative semigroup. This is achieved by applying a convolution product on definable probabilities…
The literature on Bayesian methods for the analysis of discrete-time semi-Markov processes is sparse. In this paper, we introduce the semi-Markov beta-Stacy process, a stochastic process useful for the Bayesian non-parametric analysis of…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…