1,721,096 research outputs found
Martingale representations in progressive enlargement by the reference filtration of a semi-martingale: a note on the multidimensional case
No full textLet X and Y be an m-dimensional F-semi-martingale and an n-dimensional H-semi-martingale, respectively, on the same probability space (Omega, F, P), both enjoying the predictable representation property. We propose two representation results for the square-integrable G-martingales, where G = F boolean OR H. As a first application, we identify the biggest possible value of the multiplicity in the sense of Davis and Varaiya of Vi-1(d) F-i where, fixed i is an element of (1, ..., d), F-i is the reference filtration of a martingale M-i, which enjoys the (P, F-i)-predictable representation property. This result helps us to identify a basis of martingales for the Poisson filtration enlarged by a general random time. A second application falls into the framework of credit risk modelling and in particular into the study of progressive enlargement of the market filtration by a default time. We present a new proof of the analogous of classical Kusuoka's theorem, when the risky asset price is a multidimensional semi-martingale enjoying the predictable representation property and the default time satisfies the density hypothesis
Martingale representations in progressive enlargement by multivariate point processes
No full textIn this paper, we show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove that a strong representation holds if any multivariate point process of the vector has almost surely infinite explosion time and discrete marks space. Then we provide a condition under which the components of the multidimensional local martingale driving the strong representation are pairwise orthogonal
Counting observations: A note on state estimation sensitivity with an L1-bound
No full textLet (X-t, Y-t) be a pure jump Markov process: the state X-t takes real values and the observation Y-t is a counting process. The two processes are allowed to have common jump times. Let phi (X((.))) be a functional of the state trajectory restricted to the time interval [0, T]. If we change the infinitesimal parameters and/or the initial distribution, then we introduce an error in computing the conditional law of phi (X((.))) given the observation up to time T. In this paper we give an explicit L-1-bound for this error
A Filtering Problem with Counting Observations: Approximations with Error Bounds
No full textWe consider a pure jump Markov process (Xt Yt ) with discrete state space. We suppose that the state Xt is not observable and that the observation Yt is a counting process. We construct an approximation for the filter of Xt given (Ys s ≤ t), by means of a family of piecewise constant processes, depending on the value of Yt and on the time discretization parameter. Moreover we give an explicit error bound for the convergence of the schem
Nonlinear Filtering for Markov Systems with Delayed Observations
No full textThis 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 (X, (Y) over cap), in the sense that Y-t = (Y) over cap (a)(t), 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
Approximation of nonlinear filters for Markov systems with delayed observations
No full textWe 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
Immunohistochemical detection of c-fos and c-jun oncoprotein expression in osseous and cartilaginous tumors of the skeleton
No full textNonlinear filtering for Markov systems with delayed observations
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http://www.mat.uniroma1.it/people/nappo/papers.pdf/CFN-JAMCS-DelayMarkov.pd
Transparent Conductive Oxides as Near-IR Plasmonic Materials: The Case of Al-Doped ZnO Derivatives
No full textUsing first-principles calculations, we investigate the origin of near infrared plasmonic activity in Al:ZnO transparent conducting oxides. Our results predict realistic values for the plasma frequency and the free electron density as a function of the Al doping and in agreement with recent experimental results. We also provide a microscopic insight on the formation of surface-plasmon polaritons at the Al:ZnO/ZnO interfaces in terms of characteristic lengths that can be measured by experiments. The direct comparison with standard plasmonic metals underlines the promising capabilities of transparent conducting oxides as compact and low-loss plasmonics materials for optoelectronic applications and telecommunications
Nonlinear filtering for Markov diffusion systems with delayed observations
No full textIn 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/
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