A Continuous Time Particle Filter

2009 ◽  
pp. 221-256
Author(s):  
Alan Bain ◽  
Dan Crisan
Keyword(s):  
Particle Filter ◽  
Continuous Time

Approximate MMSE and MAP estimation using continuous-time particle filter

2019 ◽  
Author(s):  
Konstantin Chugai ◽  
Ivan Kosachev ◽  
Konstantin Rybakov
Keyword(s):  
Particle Filter ◽  
Continuous Time ◽  
Map Estimation

scholarly journals A Kusuoka–Lyons–Victoir particle filter

2013 ◽  
Vol 469 (2156) ◽  
pp. 20130076 ◽  
Author(s):  
Dan Crisan ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Particle Filter ◽  
Continuous Time ◽  
Nonlinear Filtering ◽  
Computational Effort ◽  
Observation Data ◽  
Minimal Variance ◽  
Discretization Grid ◽  
Filtering Problem ◽  
Grid Mesh ◽  
Number Of Particles

The aim of this paper is to introduce a new numerical algorithm for solving the continuous time nonlinear filtering problem. In particular, we present a particle filter that combines the Kusuoka–Lyons–Victoir (KLV) cubature method on Wiener space to approximate the law of the signal with a minimal variance ‘thinning’ method, called the tree-based branching algorithm (TBBA) to keep the size of the cubature tree constant in time. The novelty of our approach resides in the adaptation of the TBBA algorithm to simultaneously control the computational effort and incorporate the observation data into the system. We provide the rate of convergence of the approximating particle filter in terms of the computational effort (number of particles) and the discretization grid mesh. Finally, we test the performance of the new algorithm on a benchmark problem (the Beneš filter).

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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