We define two new classes of stochastic processes, called tempered fractional Lévy process
of the first and second kinds (TFLP and TFLP II, respectively). TFLP and TFLP II make up …

In this paper, we study the problem of statistical inference for a continuous-time moving
average Lévy process of the form Z_t=RK(ts)\,dL_s,\qquadt∈R, with a deterministic kernel K …

Lévy-Driven Ornstein-Uhlenbeck (or CAR (1)) processes were introduced by Barndorff-
Nielsen and Shephard [1] as a model for stochastic volatility. Pham [17] developed a general …

In the modern world of “Big Data,” dynamic signals are often multivariate and characterized
by joint scale-free dynamics (self-similarity) and non-Gaussianity. In this paper, we examine …

In this paper, we construct operator fractional Lévy motion (ofLm), a broad class of infinitely
divisible stochastic processes that are covariance operator self-similar and have wide-sense …

Abstract When an Ornstein–Uhlenbeck (or CAR (1)) process is observed at discrete times 0,
h, 2 h,…[T/h] h, the unobserved driving process can be approximated from the observed …

In this article, we study the problem of parameter estimation for Ornstein–Uhlenbeck
processes of the second kind driven by α-stable Lévy motions, based on continuous and …

In the modern world, systems are routinely monitored by multiple sensors, generating “Big
Data” in the form of a large collection of time series. However, dynamic signals are often low …

This paper is concerned with parametric estimation, model specification and autocorrelation
diagnosis for stationary moving averages driven by a Wiener process. By incorporating the …

where Pa is a parametric family of probability measures on (Rd, B (Rd)), the mapping a^ Pa
(B) is measurable for any B e B (Rd), A c Rk is a set of possible values of the parameter a …