Related papers: Processes with Long Memory: Regenerative Construct…
In this paper a general approach for the perfect simulation of a stationary process with at most countable state space is outlined. The process is specified through a kernel, prescribing the probability of each state conditional to the…
We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling…
In this paper we consider the problem of determining the law of binary stochastic processes from transition kernels depending on the whole past. These kernels are linear in the past values of the process. They are allowed to assume values…
We present a perfect simulation algorithm for measures that are absolutely continuous with respect to some Poisson process and can be obtained as invariant measures of birth-and-death processes. Examples include area- and…
In this article we introduce two new perfect simulation algorithms for chains with infinite memory. Both algorithms belong to the coupling of past procedures. The novelty of our approach is that it allows to include unknown states to the…
This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…
In this paper we study stochastic process indexed by $\mathbb {Z}$ constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a…
Long memory in the sense of slowly decaying autocorrelations is a stylized fact in many time series from economics and finance. The fractionally integrated process is the workhorse model for the analysis of these time series. Nevertheless,…
We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infnite memory chains for which the family of transition probabilities is represented by a probabilistic…
Consider an irreducible, Harris recurrent Markov chain of transition kernel {\Pi} and invariant probability measure {\pi}. If {\Pi} satisfies a minorization condition, then the split chain allows the identification of regeneration times…
We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a…
We consider a particle system on $Z^d$ with finite state space and interactions of infinite range. Assuming that the rate of change is continuous and decays sufficiently fast, we introduce a perfect simulation algorithm for the stationary…
We study the problem of deinterleaving a set of finite-memory (Markov) processes over disjoint finite alphabets, which have been randomly interleaved by a finite-memory switch. The deinterleaver has access to a sample of the resulting…
This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…
In this work, we will investigate a Bayesian approach to estimating the parameters of long memory models. Long memory, characterized by the phenomenon of hyperbolic autocorrelation decay in time series, has garnered significant attention.…
We propose a new Kalikow decomposition for continuous time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation…
We consider killed Markov decision processes for countable models on a finite time-interval. Existence of a uniform $\varepsilon$-optimal policy is proven. We show the correctness of the fundamental equation. The optimal control problem is…
Inference in hidden Markov model has been challenging in terms of scalability due to dependencies in the observation data. In this paper, we utilize the inherent memory decay in hidden Markov models, such that the forward and backward…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
As the particle count escalates, the computational demands of diverse simulation algorithms surge, paralleled by a marked enhancement in accuracy. The question arises whether this heightened precision asymptotically dwindles towards zero or…