Related papers: Concatenation and Pasting of Right Processes
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
Strong approximations of uniform transport processes to the standard Brownian motion rely on the Skorokhod embedding of random walk with centered double exponential increments. In this note we make such an embedding explicit by means of a…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of…
This paper studies function approximation for finite horizon discrete time Markov decision processes under certain convexity assumptions. Uniform convergence of these approximations on compact sets is proved under several sampling schemes…
We examine data-processing of Markov chains through the lens of information geometry. We first establish a theory of congruent Markov morphisms within the framework of stochastic matrices. Specifically, we introduce and justify the concept…
The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the…
The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time,…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
For $N\in\mathbb{N}$, let $\pi_N$ be the law of the number of fixed points of a random permutation of $\{1, 2, ..., N\}$. Let $\mathcal{P}$ be a Poisson law of parameter 1.A classical result shows that $\pi_N$ converges to $\mathcal{P}$ for…
This paper consists of $3$ parts. The first part only considers classical processes and introduces two different extensions of the notion of hidden Markov process. In the second part, the notion of quantum hidden process is introduced. In…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
In this paper the class of mixed renewal processes (MRPs for short) with mixing parameter a random vector from \cite{lm6z3} (enlarging Huang's \cite{hu} original class) is replaced by the strictly more comprising class of all extended MRPs…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov…
The recent study by B. De Bruyne, S. N. Majumdar, H. Orland and G. Schehr [arXiv:2110.07573], concerning the conditioning of the Brownian motion and of random walks on global dynamical constraints over a finite time-window $T$, is…
We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…
An algorithm is proposed for computing equilibrium averages of Markov chains which suffer from metastability -- the tendency to remain in one or more subsets of state space for long time intervals. The algorithm, called the parallel replica…
In this paper, we show an approximation in law of the complex Brownian motion by processes constructed from a stochastic process with independent increments. We give sufficient conditions for the characteristic function of the process with…