scholarly journals Stability with respect to initial conditions in V-norm for nonlinear filters with ergodic observations

2017 ◽  
Vol 54 (1) ◽  
pp. 118-133 ◽  
Author(s):  
Mathieu Gerber ◽  
Nick Whiteley
Keyword(s):  
Initial Conditions ◽  
Stability Result ◽  
Initial Distribution ◽  
Nonlinear Filters ◽  
Initial Condition ◽  
Test Functions ◽  
Total Variation Norm ◽  
Variation Norm ◽  
Prediction Filter ◽  
General Setup

AbstractWe establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in V-norm, allowing for unbounded test functions. The analysis is conducted in an general setup involving nonnegative kernels in a random environment which allows treatment of filters and prediction filters in a single framework. The main result is illustrated on two examples, the first showing that a total variation norm stability result obtained by Douc et al. (2009) can be extended to V-norm without any additional assumptions, the second concerning a situation in which forgetting of the initial condition holds in V-norm for the filters, but the V-norm of each prediction filter is infinite.

scholarly journals Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity

2014 ◽  
Vol 51 (3) ◽  
pp. 756-768 ◽  
Author(s):  
Servet Martínez ◽  
Jaime San Martín ◽  
Denis Villemonais
Keyword(s):  
Total Variation ◽  
Existence And Uniqueness ◽  
Initial Distribution ◽  
Total Variation Norm ◽  
Birth And Death Processes ◽  
Long Time Behaviour ◽  
Long Time ◽  
Unique Distribution ◽  
Variation Norm ◽  
Quasistationary Distributions

We study the long-time behaviour of a Markov process evolving in N and conditioned not to hit 0. Assuming that the process comes back quickly from ∞, we prove that the process admits a unique quasistationary distribution (in particular, the distribution of the conditioned process admits a limit when time goes to ∞). Moreover, we prove that the distribution of the process converges exponentially fast in the total variation norm to its quasistationary distribution and we provide a bound for the rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasistationary distribution for birth-and-death processes: we prove that starting from any initial distribution the conditional probability converges in law to a unique distribution ρ supported in N* if and only if the process has a unique quasistationary distribution. Moreover, ρ is this unique quasistationary distribution and the convergence is shown to be exponentially fast in the total variation norm. Also, considering the lack of results on quasistationary distributions for nonirreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasistationary distribution for a class of possibly nonirreducible processes.

scholarly journals Existence and Uniqueness of a Quasistationary Distribution for Markov Processes with Fast Return from Infinity

2014 ◽  
Vol 51 (03) ◽  
pp. 756-768 ◽  
Author(s):  
Servet Martínez ◽  
Jaime San Martín ◽  
Denis Villemonais
Keyword(s):  
Total Variation ◽  
Existence And Uniqueness ◽  
Initial Distribution ◽  
Total Variation Norm ◽  
Birth And Death Processes ◽  
Long Time Behaviour ◽  
Long Time ◽  
Unique Distribution ◽  
Variation Norm ◽  
Quasistationary Distributions

We study the long-time behaviour of a Markov process evolving inNand conditioned not to hit 0. Assuming that the process comes back quickly from ∞, we prove that the process admits a uniquequasistationary distribution(in particular, the distribution of the conditioned process admits a limit when time goes to ∞). Moreover, we prove that the distribution of the process converges exponentially fast in the total variation norm to its quasistationary distribution and we provide a bound for the rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasistationary distribution for birth-and-death processes: we prove that starting from any initial distribution the conditional probability converges in law to a unique distribution ρ supported inN*if and only if the process has a unique quasistationary distribution. Moreover, ρ is this unique quasistationary distribution and the convergence is shown to be exponentially fast in the total variation norm. Also, considering the lack of results on quasistationary distributions for nonirreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasistationary distribution for a class of possibly nonirreducible processes.

Is it a Right Assumption That B and Ge are Distributed Randomly After Growing a Strained HBT-Structure?

2002 ◽  
Vol 716 ◽  
Author(s):  
Victor I. Kol'dyaev
Keyword(s):  
Surface Segregation ◽  
Initial Conditions ◽  
Initial Condition ◽  
Basic Assumptions ◽  
Transient Diffusion ◽  
Segregation Process ◽  
Main Observation

AbstractIt is accepted that surface Ge atoms are considered to be responsible for the surface B segregation process. A set of original experiments is carried out. A main observation from the B and Ge profiles grown at different conditions shows that at certain conditions B is taking initiative and determine the Ge surface segregation process. basic assumptions are suggested to self-consistently explain these original experimental features and what is observed in the literature. These results have a strong implication for modeling the B diffusion in Si1-xGex where the initial conditions should be formulated accounting for the correlation in B and Ge distribution. A new assumption for the initial condition to be “all B atoms are captured by Ge” is regarded as a right one implicating that there is no any transient diffusion representing the B capturing kinetics.

scholarly journals Application of Adjoint-Derived Forecast Sensitivities to the 24–25 January 2000 U.S. East Coast Snowstorm

2005 ◽  
Vol 133 (11) ◽  
pp. 3148-3175 ◽  
Author(s):  
Daryl T. Kleist ◽  
Michael C. Morgan
Keyword(s):  
Response Function ◽  
Initial Conditions ◽  
Forecast Error ◽  
Weather Prediction ◽  
Lower Troposphere ◽  
Vertical Motion ◽  
Initial Condition ◽  
Response Functions ◽  
Eastern United States ◽  
Surface Cyclone

Abstract The 24–25 January 2000 eastern United States snowstorm was noteworthy as operational numerical weather prediction (NWP) guidance was poor for lead times as short as 36 h. Despite improvements in the forecast of the surface cyclone position and intensity at 1200 UTC 25 January 2000 with decreasing lead time, NWP guidance placed the westward extent of the midtropospheric, frontogenetically forced precipitation shield too far to the east. To assess the influence of initial condition uncertainties on the forecast of this event, an adjoint model is used to evaluate forecast sensitivities for 36- and 48-h forecasts valid at 1200 UTC 25 January 2000 using as response functions the energy-weighted forecast error, lower-tropospheric circulation about a box surrounding the surface cyclone, 750-hPa frontogenesis, and vertical motion. The sensitivities with respect to the initial conditions for these response functions are in general very similar: geographically isolated, maximized in the middle and lower troposphere, and possessing an upshear vertical tilt. The sensitivities are maximized in a region of enhanced low-level baroclinicity in the vicinity of the surface cyclone’s precursor upper trough. However, differences in the phase and structure of the gradients for the four response functions are evident, which suggests that perturbations could be constructed to alter one response function but not necessarily the others. Gradients of the forecast error response function with respect to the initial conditions are used in an iterative procedure to construct initial condition perturbations that reduce the forecast error. These initial condition perturbations were small in terms of both spatial scale and magnitude. Those initial condition perturbations that were confined primarily to the midtroposphere grew rapidly into much larger amplitude upper-and-lower tropospheric perturbations. The perturbed forecasts were not only characterized by reduced final time forecast error, but also had a synoptic evolution that more closely followed analyses and observations.

L 1 and L ∞ stability of transition densities of perturbed diffusions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ilya Bitter ◽  
Valentin Konakov
Keyword(s):  
Linear Growth ◽  
Stability Result ◽  
Regularity Conditions ◽  
Initial Condition ◽  
Weak Regularity ◽  
Transition Densities ◽  
The Stability ◽  
Drift Terms

Abstract In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{\infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.

Transient elastodynamic analysis with a combination of convolution quadrature method and pseudo-initial condition method

2018 ◽  
Vol 36 (1) ◽  
pp. 334-355
Author(s):  
Yuan Li ◽  
J. Zhang ◽  
Yudong Zhong ◽  
Xiaomin Shu ◽  
Yunqiao Dong
Keyword(s):  
Initial Conditions ◽  
Initial Condition ◽  
Quadrature Method ◽  
Memory Requirement ◽  
Content Type ◽  
Convolution Quadrature ◽  
Force Method ◽  
Cpu Time ◽  
Condition Method ◽  
Convolution Quadrature Method

Purpose The Convolution Quadrature Method (CQM) has been widely applied to solve transient elastodynamic problems because of its stability and generality. However, the CQM suffers from the problems of huge memory requirement in case of direct implementation in time domain or CPU time in case of its reformulation in Laplace domain. The purpose of this paper is to combine the CQM with the pseudo-initial condition method (PICM) to achieve a good balance between memory requirement and CPU time. Design/methodology/approach The combined methods first subdivide the whole analysis into a few sub-analyses, which is dealt with the PICM, namely, the results obtained by previous sub-analysis are used as the initial conditions for the next sub-analysis. In each sub-analysis, the time interval is further discretized into a number of sub-steps and dealt with the CQM. For non-zero initial conditions, the pseudo-force method is used to transform them into equivalent body forces. The boundary face method is employed in the numerical implementation. Three examples are analyzed. Results are compared with analytical solutions or FEM results and the results of reformulated CQM. Findings Results demonstrate that the computation time and the storage requirement can be reduced significantly as compared to the CQM, by using the combined approach. Originality/value The combined methods can be successfully applied to the problems of long-time dynamic response, which requires a large amount of computer memory when CQM is applied, while preserving the CQM stability. If the number of time steps is high, then the accuracy of the proposed approach can be deteriorated because of the pseudo-force method.

scholarly journals Using G-Suite Docs to Improve Students’ Writing Ability at SMA Negeri 1 Batuan, Sumenep

2021 ◽  
Vol 3 (2) ◽  
pp. 1-15
Author(s):  
Norani Yanuar Subandi ◽  
Hablil Warid ◽  
Sulistyaningsih
Keyword(s):  
Action Research ◽  
Data Collection ◽  
Group Work ◽  
Initial Conditions ◽  
Research Data ◽  
Initial Condition ◽  
Writing Ability ◽  
Student Activity ◽  
School Year ◽  
Learning Management

The aim of this research were to describe the implementation of Using G - Suite Docs to Improve Students’ Writing Ability at SMA Negeri 1 Batuan, Sumenep and to find out  the achievement of student’s writing ability in Using G - Suite at SMA Negeri 1 Batuan, Sumenep. The approach used in this research was classroom action research. Data collection tools in this study were observation sheets of learning management through G-Suite Docs media, student activity observation sheets and tests. The objects of this study were 25 students of class XII IPA 1 SMA Negeri 1 Batuan even semester of the 2020/2021 school year. The research showed that the result of implementing of using G-Suite Docs showed that the students were more enthusiastic in writing discussion text and all students could respond to their group work by commenting on the process in writing. Moreover, the students achievement from the initial conditions up to second cycle. The average of initial condition was 66.6 changed to be 79.64 or increased 80% with the result of completeness reaching 92%.   Keywords: G - Suite Docs, Writing ability, Discussion Text

Role of initial condition and parametric uncertainty in a severe hailstorm forecast

2021 ◽  
Author(s):  
Patrick Kuntze ◽  
Annette Miltenberger ◽  
Corinna Hoose ◽  
Michael Kunz
Keyword(s):  
Initial Conditions ◽  
Weather Prediction ◽  
Parametric Uncertainty ◽  
Radar Data ◽  
Cloud Microphysics ◽  
Initial Condition ◽  
Relative Contribution ◽  
Cloud Properties ◽  
Set Up ◽  
The Impact

<p>Forecasting high impact weather events is a major challenge for numerical weather prediction. Initial condition uncertainty plays a major role but so potentially do uncertainties arising from the representation of physical processes, e.g. cloud microphysics. In this project, we investigate the impact of these uncertainties for the forecast of cloud properties, precipitation and hail of a selected severe convective storm over South-Eastern Germany.<br>To investigate the joint impact of initial condition and parametric uncertainty a large ensemble including perturbed initial conditions and systematic variations in several cloud microphysical parameters is conducted with the ICON model (at 1 km grid-spacing). The comparison of the baseline, unperturbed simulation to satellite, radiosonde, and radar data shows that the model reproduces the key features of the storm and its evolution. In particular also substantial hail precipitation at the surface is predicted. Here, we will present first results including the simulation set-up, the evaluation of the baseline simulation, and the variability of hail forecasts from the ensemble simulation.<br>In a later stage of the project we aim to assess the relative contribution of the introduced model variations to changes in the microphysical evolution of the storm and to the fore- cast uncertainty in larger-scale meteorological conditions.</p>

Dependence of global monsoon response to volcanic eruptions on the background oceanic states

2021 ◽  
Author(s):  
Meng Zuo ◽  
Tianjun Zhou ◽  
Wenmin Man
Keyword(s):  
Radiative Forcing ◽  
Initial Conditions ◽  
Southern Oscillation ◽  
Volcanic Eruptions ◽  
Initial Condition ◽  
Monsoon Precipitation ◽  
Surface Cooling ◽  
Global Monsoon ◽  
Precipitation Changes ◽  
Sst Anomalies

<p>Both proxy data and climate modeling show divergent responses of global monsoon precipitation to volcanic eruptions. The reason is however unknown. Here, based on analysis of the CESM Last Millennium Ensemble simulation, we show evidences that the divergent responses are dominated by the pre-eruption background oceanic states. We found that under El Niño-Southern Oscillation (ENSO) neutral and warm phases initial conditions, the Pacific favors an El Niño-like anomaly after volcanic eruptions, while La Niña-like SST anomalies tend to occur following eruptions under ENSO cold phase initial condition, especially after southern eruptions. The cold initial condition is associated with stronger upper ocean temperature stratification and shallower thermocline over the eastern Pacific than normal. The easterly anomalies triggered by surface cooling over the tropical South America continent can generate changes in SST through anomalous advection and the ocean subsurface upwelling more efficiently, causing La Niña-like SST anomalies. Whereas under warm initial condition, the easterly anomalies fail to develop and the westerly anomalies still play a dominant role, thus forms an El Niño-like SST anomaly. Such SST response further regulates the monsoon precipitation changes through atmospheric teleconnection. The contribution of direct radiative forcing and indirect SST response to precipitation changes show regional differences, which will further affect the intensity and sign of precipitation response in submonsoon regions. Our results imply that attention should be paid to the background oceanic state when predicting the global monsoon precipitation responses to volcanic eruptions.</p>

scholarly journals Imaging Noise Suppression: Fourth-Order Partial Differential Equations and Travelling Wave Solutions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2019
Author(s):  
Sameerah Jamal
Keyword(s):  
Fourth Order ◽  
Noise Suppression ◽  
Linear Equations ◽  
Travelling Wave ◽  
Order Partial Differential Equation ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Total Variation Norm ◽  
Wave Solutions ◽  
Variation Norm

In this paper, we discuss travelling wave solutions for image smoothing based on a fourth-order partial differential equation. One of the recurring issues of digital imaging is the amount of noise. One solution to this is to minimise the total variation norm of the image, thus giving rise to non-linear equations. We investigate the variational properties of the Lagrange functionals associated with these minimisation problems.

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