Optimal linear estimators for systems with random measurement delays

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.

A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE

In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).

Phase retrieval with PhaseLift algorithm

This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the phase retrieval problem can be transformed into the low rank matrix recovery problem and then be solved by convex programming known as PhaseLift.Thus,stable guarantees for such problem have been gradually established for measurements sampled from sufficiently random distribution,for instance,the standard normal distribution.Further,exact recovery results have also been set up for masked Fourier measurements which are closely related to practical applications.

MULTIFRACTAL DECOMPOSITION OF CERTAIN RECURSIVE SETS WITHOUT THE OPEN SET CONDITION

The open set condition is the weakest condition hitherto in multifractal decomposition on the recursive sets. This paper deals with certain recursive fractals which have no relevence to the separation condition and gives their multifractal decomposition.

Ito Formula for Integral Processes Related to Space-Time Levy Noise

In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON-PISOT NUMBERS

The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper,we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions,if they exist,are not L 2. We also construct other Bernolulli convolutions whose density functions,if they exist,behave rather badly.

The Construction of Statisticaly Self-similar Measures

We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statistically self similar sets as well.

Convex Reconstruction of Structured Matrix Signals from Linear Measurements:Theoretical Results

The problem of reconstructing n-by-n structured matrix signal X=(x1,...,xn)via convex optimization is investigated,where each column xj is a vector of s-sparsity and all columns have the same l1-norm value.In this paper,the convex programming problem was solved with noise-free or noisy measurements.The uniform sufficient conditions were established which are very close to necessary conditions and non-uniform conditions were also discussed.In addition,stronger conditions were investigated to guarantee the reconstructed signal’s support stability,sign stability and approximation-error robustness.Moreover,with the convex geometric approach in random measurement setting,one of the critical ingredients in this contribution is to estimate the related widths’bounds in case of Gaussian and non-Gaussian distributions.These bounds were explicitly controlled by signal’s structural parameters r and s which determined matrix signal’s column-wise sparsity and l1-column-flatness respectively.This paper provides a relatively complete theory on column-wise sparse and l1-column-flat matrix signal reconstruction,as well as a heuristic foundation for dealing with more complicated high-order tensor signals in,e.g.,statistical big data analysis and related data-intensive applications.

An Averaging Principle for Caputo Fractional Stochastic Differential Equations with Compensated Poisson Random Measure

This article deals with an averaging principle for Caputo fractional stochastic differential equations with compensated Poisson random measure.The main contribution of this article is impose some new averaging conditions to deal with the averaging principle for Caputo fractional stochastic differential equations.Under these conditions,the solution to a Caputo fractional stochastic differential system can be approximated by that of a corresponding averaging equation in the sense ofmean square.

Bernoulli particle flter with observer altitude for maritime radiation source tracking in the presence of measurement uncertainty

For maritime radiation source target tracking in particular electronic counter measures（ECM）environment,there exists two main problems which can deteriorate the tracking performance of traditional approaches.The frst problem is the poor observability of the radiation source.The second one is the measurement uncertainty which includes the uncertainty of the target appearing/disappearing and the detection uncertainty（false and missed detections）.A novel approach is proposed in this paper for tracking maritime radiation source in the presence of measurement uncertainty.To solve the poor observability of maritime radiation source target,using the radiation source motion restriction,the observer altitude information is incorporated into the bearings-only tracking（BOT）method to obtain the unique target localization.Then the two uncertainties in the ECM environment are modeled by the random fnite set（RFS）theory and the Bernoulli fltering method with the observer altitude is adopted to solve the tracking problem of maritime radiation source in such context.Simulation experiments verify the validity of the proposed approach for tracking maritime radiation source,and also demonstrate the superiority of the method compared with the traditional integrated probabilistic data association（IPDA）method.The tracking performance under different conditions,particularly those involving different duration of radiation source opening and switching-off,indicates that the method to solve our problem is robust and effective.

BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH RANDOM MEASURES

Backward stochastic differential equations (BSDE) are discussed in many papers. However, in those papers, only Brownian motion and Poisson process are considered. In this paper, we consider BSDE driven by continuous local martingales and random measures.

Hölder Continuity of Solutions of SPDEs with Reflection

In this paper,we obtain the Hölder continuity of the solutions of SPDEs with reflection,which have singular drifts(random measures).

Transportation Cost Inequalities for Stochastic Reaction-Diffusion Equations with Lévy Noises and Non-Lipschitz Reaction Terms

For stochastic reaction-diffusion equations with Levy noises and non-Lipschitz reaction terms,we prove that W\H transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the L1-metrie.The proofs are based on the Galerkin approximations.

Stochastic Fubini Theorem for Jump Noises in Banach Spaces

We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which extends this classical result from Hilbert space setting to Banach space setting.

Detecting the filamentary structure of 3D point clouds:Proposal of a wavelet-based method

The analysis of the filamentary structure of the cosmo as well as that of the internal structure of the polar ice suggests the development of models based on three-dimensional(3D)point processes.A point process,regarded as a random measure,can be expressed as a sum of Delta Dirac measures concentrated at some random points.The integration with respect to the point process leads the continuous wavelet transform of the process itself.As possible mother wavelets,we propose the application of the Mexican hat and the Morlet wavelet in order to implement the scale-angle energy density of the process,depending on the dilation parameter and on the three angles which define the direction in the Euclidean space.Such indicator proves to be a sensitive detector of any variation in the direction and it can be successfully implemented to study the isotropy or the filamentary structure in 3D point patterns.

Moderate deviations for neutral functional stochastic differential equations driven by Levy noises

Using the weak convergence method introduced by A.Budhiraja,P.Dupuis,and A.Ganguly[Ann.Probab.,2016,44:1723-1775],we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH BROWNIAN MOTION AND POISSON PROCESS

Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathemstical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper.