Compressed sensing is a recently developed signal acquisition technique. In contrast to traditional sampling methods, significantly fewer samples are required whenever the signals admit a sparse representation. Crucially, sampling methods can be constructed that allow the reconstruction of sparse signals from a small number of measurements using efficient algorithms. We have recently generalise...

This paper presents the problem of nonlinear observer design for a class of time-delay nonlinear systems with uncertainty. The nonlinearity of this class of systems has to satisfy the Lipschitz condition whilst the uncertain term is a bounded function. Various performance indices are analysed to test the stability of the error system when all nonlinear terms satisfying the Lipschitz condition. ...

Abstract. We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under suitable conditions. The results are applied to stochastic equations driven by one-sided Lévy processes and those of continuous state branching proces...

This paper examines a continuous time intertemporal consumption and portfolio choice problem with stochastic differential utility preference of Epstein–Zin type for robust investor, who worries about model misspecification seeks decision rules. We provide verification theorem which formulates the Hamilton–Jacobi–Bellman–Isaacs equation under non-Lipschitz condition. Then, theorem, explicit clos...

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival...