Related papers: A new look at perfect simulation for chains with i…
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…
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…
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…
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 establish sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. The new assumption, localized continuity, is formalized with the help of the notion of context trees, and includes the…
We explicitly construct a coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of…
We show that any application of the technique of unbiased simulation becomes perfect simulation when coalescence of the two coupled Markov chains can be practically assured in advance. This happens when a fixed number of iterations is high…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the…
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 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 paper, we study inference for chains of variable order under two distinct contamination regimes. Consider we have a chain of variable memory on a finite alphabet containing zero. At each instant of time an independent coin is…
Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the…
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…
We consider a new class of interacting particle systems with a countable number of interacting components. The system represents the time evolution of the membrane potentials of an infinite set of interacting neurons. We prove the existence…
We develop exact simulation (also known as perfect sampling) algorithms for a family of assemble-to-order systems. Due to the finite capacity, and coupling in demands and replenishments, known solving techniques are inefficient for larger…
We study a class of interacting nonlinear Hawkes point processes on the integer lattice in which each component is reset after its own jumps. The intensity of a component depends on the post-reset activity of its nearest neighbours, which…
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…
Stochastic processes underlie a vast range of natural and social phenomena. Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g. traffic congestion, are effectively probabilistic because we…
We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence.…