Nonlinear filtering for Markov systems with delayed observations

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Retrospective French nationwide survey of childhood aggressive vascular anomalies of bone, 1988-2009

<p>Abstract</p> <p>Objective</p> <p>To document the epidemiological, clinical, histological and radiological characteristics of aggressive vascular abnormalities of bone in children.</p> <p>Study design</p> <p>Correspondents of the French Society of Childhood Malignancies were asked to notify all cases of aggressive vascular abnormalities of bone diagnosed between January 1988 and September 2009.</p> <p>Results</p> <p>21 cases were identified; 62% of the patients were boys. No familial cases were observed, and the disease appeared to be sporadic. Mean age at diagnosis was 8.0 years [0.8-16.9 years]. Median follow-up was 3 years [0.3-17 years]. The main presenting signs were bone fracture (n = 4) and respiratory distress (n = 7), but more indolent onset was observed in 8 cases. Lung involvement, with lymphangiectasies and pleural effusion, was the most frequent form of extraosseous involvement (10/21). Bisphosphonates, alpha interferon and radiotherapy were used as potentially curative treatments. High-dose radiotherapy appeared to be effective on pleural effusion but caused major late sequelae, whereas antiangiogenic drugs like alpha interferon and zoledrenate have had a limited impact on the course of pulmonary complications. The impact of bisphosphonates and alpha interferon on bone lesions was also difficult to assess, owing to insufficient follow-up in most cases, but it was occasionally positive. Six deaths were observed and the overall 10-year mortality rate was about 30%. The prognosis depended mainly on pulmonary and spinal complications.</p> <p>Conclusion</p> <p>Aggressive vascular abnormalities of bone are extremely rare in childhood but are lifethreatening. The impact of anti-angiogenic drugs on pulmonary complications seems to be limited, but they may improve bone lesions.</p

Observation-Parameterised Risk-Sensitive State Estimation with Correlated Noise Processes

In this article we consider risk sensitive filtering and smoothing for a nonlinear scalar-valued dynamical system with correlated state and observer noise processes. The model we consider is an Itô diffusion state process observed through a Wiener proce

Nonlinear filtering for Markov diffusion systems with delayed observations

In this paper, we consider a nonlinear filtering problem when the state process is a diffusion X-t and the observations start at a fixed time tau and from that time on depend on the delayed process Xt-tau

Approximation of nonlinear filters for Markov systems with delayed observations

The aim of this paper is to give some approximation results for a class of nonlinear filtering problems with delay in the observation. First, we point out some general results on the approximation problem for the filter in nonlinear filtering. In particular, we give a general procedure for obtaining some upper bounds for the different approximations we consider. This procedure is then applied in the case of nonlinear filtering problems with delay $(X,Y)$, which can be represented by means of a Markov system $(X,\hat{Y})$, in the sense that $Y_{t}=\hat{Y}_{a(t)}$. Finally, these upper bounds are computed explicitly in the particular case of Markov jump process with counting observations

Approximation of nonlinear filters for Markov systems with delayed observations

We obtain some approximation results for a class of nonlinear filtering problems with delay in the observation, i.e. systems (X, Y), which can be represented by means of a Markov system (X, (Y) over cap), in the sense that Y(t) = (Y) over cap (a)(t). To this aim we give some general upper bounds which are computed explicitly in the particular case of Markov jump processes with counting observations

Nonlinear filtering for Markov systems with delayed observations

This paper deals with nonlinear filtering problems with delays, i.e., we consider a system (X,Y ), which can be represented by means of a system [...], in the sense that [...], where a(t) is a delayed time transformation. We start with X being a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory. Various assumptions on the function a(t) are considered

Nonlinear filtering for Markov diffusion systems with delayed observations

In this paper, we consider a nonlinear filtering problem when the state process is a diffusion X-t and the observations start at a fixed time tau and from that time on depend on the delayed process Xt-tau

Nonlinear filtering for Markov diffusion systems with delayed observations

In this paper, we consider a nonlinear filtering problem when the state process is a diffusion X/sub t/ and the observations start at a fixed time T and from that time on depend on the delayed process X/sub t-T/