Subordinator

About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.

Convergence results for the time-changed fractional Ornstein–Uhlenbeck processes

Abstract: In this paper we study some convergence results concerning the one-dimensional distribution of a time-changed fractional Ornstein-Uhlenbeck process. In particular, we establish that, despite the time change, the process admits a Gaussian limit random variable. On the other hand, we prove that the process converges towards the time-changed Ornstein-Uhlenbeck as the Hurst index $H \to 1/2^+$, with locally uniform convergence of one-dimensional distributions. Moreover, we also achieve convergence in the Skorohod $J_1$-topology of the time-changed fractional Ornstein-Uhlenbeck process as $H \to 1/2^+$ in the space of cadlag functions. Finally, we exploit some convergence properties of mild solutions of a generalized Fokker-Planck equation associated to the aforementioned processes, as $H \to 1/2^+$.

Parametric inference for discretely observed subordinate diffusions

Abstract: Subordinate diffusions are constructed by time changing diffusion processes with an independent Levy subordinator. This is a rich family of Markovian jump processes which exhibit a variety of jump behavior and have found many applications. This paper studies parametric inference of discretely observed ergodic subordinate diffusions. We solve the identifiability problem for these processes using spectral theory and propose a two-step estimation procedure based on estimating functions. In the first step, we use an estimating function that only involves diffusion parameters. In the second step, a martingale estimating function based on eigenvalues and eigenfunctions of the subordinate diffusion is used to estimate the parameters of the Levy subordinator and the problem of how to choose the weighting matrix is solved. When the eigenpairs do not have analytical expressions, we apply the constant perturbation method with high order corrections to calculate them numerically and the martingale estimating function can be computed efficiently. Consistency and asymptotic normality of our estimator are established considering the effect of numerical approximation. Through numerical examples, we show that our method is both computationally and statistically efficient. A subordinate diffusion model for VIX (CBOE volatility index) is developed which provides good fit to the data.

A block replacement policy for a bivariate wear subordinator

Abstract: Classical models for wear accumulative indicators are univariate Gamma and compound Poisson processes, which both are univariate subordinators (increasing Levy processes). Bivariate subordinators are here proposed to model correlated couples of univariate wear indicators, namely bivariate wear indicators. A few properties of these bivariate subordinators are pointed out, and a special simple construction is provided, for application purpose. The use of these bivariate wear subordinors is illustrated through the study of a classical block replacement policy. The influence of the dependence between the marginal indicators on the optimal block replacement policy is pointed out.

From embedded propositions to complex predicates

Abstract: Abstract This article examines verbal sequences in Arabic dialects which can correspond either to complex sentences with embedded clauses or to complex predicates with reduction of one or the other verb. The first part is devoted to complex sentences where completives and subordinates of purpose and consequence are introduced by a marker that is generally specific, but sometimes polyfunctional. The second part explores embedding without a subordinator (with distinct or identical subjects), as well as with cases of complex predicates, sometimes with reduction of V1 (cases of auxiliarization and pragmatization), sometimes of V2 (rare cases of serial verbs).

Extreme Statistics of Superdiffusive Lévy Flights and Every Other Lévy Subordinate Brownian Motion

Abstract: The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher randomly explores a spatial domain for a randomly located target. There has been significant interest and controversy regarding optimal search strategies, especially for superdiffusive processes. The optimal search strategy is typically defined as the strategy that minimizes the time it takes a given single searcher to find a target, which is called a first hitting time (FHT). However, many systems involve multiple searchers, and the important timescale is the time it takes the fastest searcher to find a target, which is called an extreme FHT. In this paper, we study extreme FHTs for any stochastic process that is a random time change of Brownian motion by a Lévy subordinator. This class of stochastic processes includes superdiffusive Lévy flights in any space dimension, which are processes described by a Fokker–Planck equation with a fractional Laplacian. We find the short-time distribution of a single FHT for any Lévy subordinate Brownian motion and use this to find the full distribution and moments of extreme FHTs as the number of searchers grows. We illustrate these rigorous results in several examples and numerical simulations.