Related papers: Input estimation from discrete workload observatio…
State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state…
Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…
With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of…
Let $\{D(s), s \geq 0\}$ be a non-decreasing L\'evy process. The first-hitting time process $\{E(t) t \geq 0\}$ (which is sometimes referred to as an inverse subordinator) defined by $E(t) = \inf \{s: D(s) > t \}$ is a process which has…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…
The concept of a L\'evy subordinator is generalized to a family of non-decreasing stochastic processes, which are parameterized in terms of two Bernstein functions. Whereas the independent increments property is only maintained in the…
We describe an Euler scheme to approximate solutions of L\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the…
In this paper, we study Markov-dependent reflected autoregressive processes, and other related models the analysis of which results in a vector-valued fixed-point functional equation of a certain type. In queueing terms, such processes…
We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'{e}vy process $Y(t)$ which is reflected at 0. When the exponential clock…
We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…
For an arbitrary L\'evy process $X$ which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of $X$…
In this paper, we consider possibly misspecified stochastic differential equation models driven by L\'{e}vy processes. Regardless of whether the driving noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate unknown…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
We consider a L\'evy driven continuous time moving average process $X$ sampled at random times which follow a renewal structure independent of $X$. Asymptotic normality of the sample mean, the sample autocovariance, and the sample…
Interleaving is an online evaluation approach for information retrieval systems that compares the effectiveness of ranking functions in interpreting the users' implicit feedback. Previous work such as Hofmann et al (2011) has evaluated the…
The Exponentially Weighted Average (EWA) of observations is known to be state-of-art estimator for tracking expectations of dynamically varying data stream distributions. However, how to devise an EWA estimator to rather track quantiles of…
Distributional properties -including Laplace transforms- of integrals of Markov processes received a lot of attention in the literature. In this paper, we complete existing results in several ways. First, we provide the analytical solution…