Related papers: D-optimal designs for complex Ornstein-Uhlenbeck p…
We discuss approaches to computing eigenfunctions of the Ornstein--Uhlenbeck (OU) operator in more than two dimensions. While the spectrum of the OU operator and theoretical properties of its eigenfunctions have been well characterized in…
In this study we define a three-step procedure to relate the self-decomposability of the stationary law of a generalized Ornstein-Uhlenbeck process to the law of the increments of such processes. Based on this procedure and the results of…
Complex systems often involve random fluctuations for which self-similar properties in space and time play an important role. Fractional Brownian motions, characterized by a single scaling exponent, the Hurst exponent $H$, provide a…
In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is…
When stock prices are observed at high frequencies, more information can be utilized in estimation of parameters of the price process. However, high-frequency data are contaminated by the market microstructure noise which causes significant…
We study a least squares estimator $\hat {\theta}_T$ for the Ornstein-Uhlenbeck process, $dX_t=\theta X_t dt+\sigma dB^H_t$, driven by fractional Brownian motion $B^H$ with Hurst parameter $H\ge \frac12$. We prove the strong consistence of…
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…
An $N$-particle system with stochastic interactions is considered. Interactions are driven by a Brownian noise term and total energy conservation is imposed. The evolution of the system, in velocity space, is a diffusion on a…
In the chemical, pharmaceutical, and food industries, sometimes the order of adding a set of components has an impact on the final product. These are instances of the order-of-addition (OofA) problem, which aims to find the optimal sequence…
We consider the problem of designing experiments for investigating particle in-flight properties in thermal spraying. Observations are available on an extensive design for an initial day and thereafter in limited number for any particular…
Regression curves for studying trait relationships are developed herein. The adaptive evolution model is considered an Ornstein-Uhlenbeck system whose parameters are estimated by a novel engagement of generalized least-squares and…
We investigate the asymptotic behavior of the maximum likelihood estimators of the unknown parameters of positive recurrent Ornstein-Uhlenbeck processes driven by Ornstein-Uhlenbeck processes.
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in…
We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein--Uhlenbeck process driven by mixed fractional Brownian motion.
In recent years there have been many proposals as flexible alternatives to Gaussian based continuous time stochastic volatility models. A great deal of these models employ positive L\'evy processes. Among these are the attractive…
Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian $D$-optimality for non-linear regression models with covariates subject to measurement errors.…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
We study the first-passage dynamics of a non-Markovian stochastic process with time-averaged feedback, which we model as a one-dimensional Ornstein--Uhlenbeck process wherein the particle drift is modified by the empirical mean of its…
Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to L\'evy-driven…
A.N. Kolmogorov proposed several problems on stochastic processes, which has been rarely addressed later on. One of the open problems are stochastic processes with discontinuous covariance function. For example, semicontinuous covariance…