Interacting Particle Filtering with Discrete-Time Observations: Asymptotic Behaviour in the Gaussian Case

2001 ◽  
pp. 101-122 ◽  
Author(s):  
Pierre Del Moral ◽  
Jean Jacod
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Particle Filtering ◽  
Interacting Particle ◽  
Discrete Time Observations ◽  
Gaussian Case

Some ARMA models for dependent sequences of poisson counts

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Joint Distribution ◽  
Autoregressive Process ◽  
Two Dimensional ◽  
Arma Models ◽  
Time Reversibility ◽  
Vector Autoregressive ◽  
Arma Processes ◽  
Vector Autoregressive Process

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

scholarly journals Effect of discrete time observations on synchronization in Chua model and applications to data assimilation

2012 ◽  
Vol 22 (2) ◽  
pp. 023125 ◽  
Author(s):  
Md. Nurujjaman ◽  
Sumanth Shivamurthy ◽  
Amit Apte ◽  
Tanu Singla ◽  
P. Parmananda
Keyword(s):  
Data Assimilation ◽  
Discrete Time ◽  
Discrete Time Observations

Estimation of critical values in interacting particle systems

2000 ◽  
Vol 37 (01) ◽  
pp. 118-125
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Gerardo Sanz
Keyword(s):  
Computer Simulation ◽  
Asymptotic Behaviour ◽  
Interacting Particle Systems ◽  
Particle System ◽  
Particle Systems ◽  
Critical Values ◽  
Interacting Particle System ◽  
Absorption Time ◽  
Interacting Particle ◽  
Absorbing State

The estimation of critical values is one of the most interesting problems in the study of interacting particle systems. The bounds obtained analytically are not usually very tight and, therefore, computer simulation has been proved to be very useful in the estimation of these values. In this paper we present a new method for the estimation of critical values in any interacting particle system with an absorbing state. The method, based on the asymptotic behaviour of the absorption time of the process, is very easy to implement and provides good estimates. It can also be applied to processes different from particle systems.

scholarly journals Pólya Urns Via the Contraction Method

2014 ◽  
Vol 23 (6) ◽  
pp. 1148-1186 ◽  
Author(s):  
MARGARETE KNAPE ◽  
RALPH NEININGER
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Normal Limit ◽  
Rooted Trees ◽  
Limit Laws ◽  
Contraction Method ◽  
Limit Distributions

We propose an approach to analysing the asymptotic behaviour of Pólya urns based on the contraction method. For this, a new combinatorial discrete-time embedding of the evolution of the urn into random rooted trees is developed. A decomposition of these trees leads to a system of recursive distributional equations which capture the distributions of the numbers of balls of each colour. Ideas from the contraction method are used to study such systems of recursive distributional equations asymptotically. We apply our approach to a couple of concrete Pólya urns that lead to limit laws with normal limit distributions, with non-normal limit distributions and with asymptotic periodic distributional behaviour.

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