Del Moral, P.: 1998, Measure valued processes and interacting particle systems, Ann. Appl.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a sum and sampling from p(x k jx k 1 ; z k ) is possible. An example of an application when x k is a member of a nite set is a Jump Markov Linear System for tracking maneuvering targets [15] Analytic evaluation is possible for a second class of models for which p(x k jx k 1 ; z k ) is Gaussian [12, 9]. This can occur if the dynamics are nonlinear and the measurements linear. Such a system is given by x k = f k (x k 1 ) v k 1 ; v k 1 N (v k 1 ; 0nv 1 ; Q k 1 ) z k = H k x k n k ; n k N (n k ; 0nn 1 ; R k ) 27) is a nonlinear function, H k 2 nz nx is an observation matrix, and v ....

P Del Moral, Measure Valued Processes and Interacting Particle Systems. Application to Nonlinear Filtering Problems. Annals of Applied Probability, 1998, Volume 8, No2, pp 438-495.

....discrete modal state (de ning the maneuver index) is tracked using a particle lter and (conditioned on the maneuver index) the continuous base state is tracked using a Kalman lter. Analytic evaluation is possible for a second class of models for which p(x k jx k 1 ; z k ) is Gaussian [12] [9]. This can occur if the dynamics are non linear and the measurements linear. Such a system is given by x k =f k (x k 1 ) v k 1 ; 54) z k =H k x k n k ; 55) v k 1 N (v k 1 ; 0nv 1 ; Q k 1 ) 56) n k N (n k ; 0nn 1 ; R k ) 57) and f k : is a non linear function, H k 2 nz nx is ....

P Del Moral, Measure Valued Processes and Interacting Particle Systems. Application to Non-linear Filtering Problems. Annals of Applied Probability, 1998, Volume 8, No2, pp 438-495.

....[23] a specific methodology is described to arrive at a finite dimensional approximating filter. Alternatively, always for problems already in discrete time, one could also use the recent so called particle approach to nonlinear filtering, that is based on a simulation methodology (see e.g.[11]) 16 4 Conclusion We have considered a version of the Heath Jarrow Morton model with a volatility depending on time to maturity, the instantaneous spot rate and one fixed maturity forward rate. We have seen how estimation of this model may be set up as a non linear filtering problem under the ....

P.Del Moral, Measure valued processes and interacting particle systems. Applications to nonlinear filtering problems , Ann.Appl.Probab., 8, 438-495, 1998.

....mainly rely on improved importance sampling resampling strategies and MCMC steps. Of all the algorithms available, the most extensively studied is the bootstrap filter (Gordon, Salmond Smith, 1993) also known as the interacting particle systems resolution algorithm; see (Del Moral, 1996; Del Moral, 1997) and subsequent papers. In (Crisan, Del Moral Lyons, 1999) a rigorous treatment is given to a whole class of SMC methods. This class of methods does not however include most of the characteristics of standard methods commonly used by practitioners (Doucet, de Freitas Gordon, 2001) The aim of ....

Del Moral P. (1997) Measure valued processes and interacting particle systems. Application to non linear filtering problems. Ann. Appl. Proba., 8, 438-495.

....examples. To overcome the curse of dimensionality, interacting particle methods have been recently proposed in Gordon, Salmond and Smith [3] see also Kitagawa [4] to approximate nonlinear filtering equations, and have been thoroughly studied for discrete time models, in Del Moral [5, 6] and in Del Moral and Guionnet [7, 8] 2. Interacting particle methods For any probability distribution 2 P , let S N ( denote the empirical distribution of an N sample f i ; i = 1; Delta Delta Delta ; Ng of i.i.d. random variables with common probability distribution , i.e. S N ....

P. DEL MORAL, "Measure valued processes and interacting particle systems. Application to nonlinear filtering problems," Publication du Laboratoire de Statistique et Probabilit 'es 15--96, Universit'e Paul Sabatier, Toulouse, 1996.

No context found.

P. Del Moral, Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems. Ann. Appl. Probab. 8 (1998), no. 2, 438--495.

No context found.

P. Del Moral. Measure valued processes and interacting particle systems. Application to non-linear filtering problems, Ann. Applied Probab. vol. 8, n. 2, pp. 438--495, 1998.

No context found.

P. Del Moral. Measure valued processes and interacting particle systems. Application to non linear filtering problems. The Annals of Applied Probability, 8(2):438--495, 1998.

No context found.

P. Del Moral, Measure valued processes and interacting particle systems. Application to non linear filtering problems, Annals of Applied Probab., vol. 8, no. 2, pp. 438--495 (1998).

No context found.

P. Del Moral. Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems, Publications du Laboratoire de Statistiques et Probabilites, Universite Paul Sabatier, No 15-96, 1996.

No context found.

DEL MORAL P. (1996). Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems. Publications du Laboratoire de Statistiques et Probabilites, Universite Paul Sabatier, No 15-96. To appear in Annals of Applied Proba.

....random variables with common law Phi n (m( n Gamma1 ) where Phi n : P(E) P(E) n 1, is a given collection of sufficiently regular functions, that are dictated by the GA operators and parameters (see section 7. 1) This quite general interacting particle system model has been introduced in [10, 11]. Its asymptotic behavior as N 1 is now well understood. In some sense to be defined the empirical measures j N n def = m( n ) n 0; converge as the number of particles N 1 to a deterministic flow of distributions j n 2 P(E) n 0; solution of the measure valued dynamical system j n = ....

....the limit theorems presented in this preliminary section 6 result from collaborations of one of the authors with Alice Guionnet, Michel Ledoux and Laurent Miclo. Only a selection of existing results is presented. More information and detailed proofs can be founded in the set of referenced papers [1, 2, 3, 4, 6, 7, 10, 11]. All these developments offer the appropriate theoretical background to analyze the asymptotic behavior of GA. They also permit us to construct new genetic type methods. In section 7 we present several generic GAs which fit into our framework including the simple GA with classical mutation and ....

[Article contains additional citation context not shown here]

P. Del Moral. Measure Valued Processes and Interacting Particle Systems. Application to nonlinear Filtering Problems. Ann. Appl. Probab. 8 (1998), no. 2, 438--495.

....of the Kushner Stratonovitch equation. Here the particles move according the law of the signal, independently of each other and, after fixed length intervals they branches. In this situation suitably defined exponential weights characterize the mean number of offsprings of a given particle. In [8], and [9] the author proposes an interacting particle system approach to solve general discrete time filtering problems. In this situation the evolution of the particles depends on the past configuration of the system and the interaction function depends on suitably defined exponential weights. ....

....result we will use the Ocone Pardoux study [15] of the asymptotic stability of the optimal filtering process with respect to its initial condition. The first convergence results of the branching and the interacting particle systems approximations are described respectively in [3] 4] 5] and [7] [8]. Nevertheless the essential and unsolved problem for these particle approximations is to find conditions under which they converge in law uniformly with respect to time. The Theorem presented in this paper shows that the uniform convergence of a Monte Carlo particle approximation depends on a ....

P. Del Moral, Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems, Publications du Laboratoire de Statistiques et Probabilit'es, Universit'e Paul Sabatier, No 15-96.

....13] including Radar Sonar signal processing and GPS INS integrations. Other comparisons and examples where the extended Kalman filter fails can be found in [4] The present paper is concerned with the genetic type interacting particle systems introduced in [15] We have shown in our earlier papers [15, 16] that, under rather general assumptions, the particle density profiles converge to the desired conditional distributions of the signal when the number of particles is growing. The study of the convergence of the empirical measure on path space and large deviation principles are presented in [19] ....

....system of particles undergoing adaptation in a time varying and random environment. This environment is represented by the observation data and the form of noise source. Several convergence theorems ensuring the convergence of the particle scheme toward the desired distribution were obtained in [15, 16, 18] and [19] The results presented in this paper makes it possible to estimate the deviations up to order p N between j N ( 0;T ] and j [0;T ] The paper has the following structure: In section 2 we recall the classical formulation of the filtering problem and the interacting particle ....

[Article contains additional citation context not shown here]

DEL MORAL P. (1996). Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems. Publications du Laboratoire de Statistiques et Probabilit'es, Universit'e Paul Sabatier, No 15-96. To appear in Annals of Applied Proba.

....of the particle systems can be shown to converge to the solution of the measure valued dynamical system the evolution of the conditional distributions. In this paper we design a particle system approach which allows us to combine the branching and interacting mechanisms introduced in [4, 5, 6] [11, 12, 13, 14, 15] and in [17] Our particle approximations also cope with discrete time filtering problems in which the signal is a non linear process with transitions that depend on all the data observed in the past. The discrete time and measure valued processes under study also arise in Statistical Physics. In ....

....b N n depends on the entire configuration b n of the system. In other words between branching corrections the particle system behaves itself as a interacting particle system. The above BIPS model enables a unified description of the various particle system approximations presented in [4, 5, 6] [11, 12, 13, 14] and in [17] We have deliberately left open the question of the choice of the branching correction transition and we will devote a subsection to present several natural choices which can be used in practice. Before that, let us point out some important properties of the BIPS algorithm. ....

[Article contains additional citation context not shown here]

DEL MORAL P. (1996). Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems.Publications du Laboratoire de Statistiques et Probabilit'es, Universit'e Paul Sabatier, No 15-96, To appear in Annals of Applied Probability.

No context found.

Del Moral, P.: 1998, Measure valued processes and interacting particle systems, Ann. Appl.

No context found.

Del Moral P. Measure-valued processes and interacting particule systems. Application to nonlinear filtering problems. The Annals of Applied Probability, vol. 8, No2, 438-495, 1998.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC