1,721,048 research outputs found
Martingale Approach for Modeling DNA Synthesis
No full textGerardi, A.; Nappo, G.. (1987). Martingale Approach for Modeling DNA Synthesis. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/4527
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-t and the observations start at a fixed time tau and from that time on depend on the delayed process Xt-tau
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
Robust approximation in a filtering problem with real state space and counting observations
No full textLet (X-t, Y-t) be a pure jump Markov process, where X-t takes values in R and Y-t is a counting process. We compare the filter of this system and a filter of a suitably modified system. We compute an explicit bound for the distance in the so-called bounded Lipschitz metric between the two filters. Finally we show how to use this bound to construct a discrete space approximation of the filter
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: Error Bounds due to the Uncertainty on the Infinitesimal Parameters
No full textLet(X Y) be a pure jump Markov process with discrete state space. Let the state X be not bservable and the observation Y be accounting process. We are interested in the filter of X given Y and initsdependence on the model. More precisely we compare this filter with the filter of another system which differs from the previous one only by the infinitesimal parameters and the initial distribution, and we give anexplicit bound for the distance in variation norm between the two filters. Finally we use this bound to examine how much a discrete time approximation procedure is affected by a slight error in the model and, in a special case, to examine the error due to the use of a finite state space model instead of an infinite one
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
- …
