scholarly journals Joint law of an Ornstein–Uhlenbeck process and its supremum

2020 ◽  
Vol 57 (2) ◽  
pp. 541-558
Author(s):  
Christophette Blanchet-Scalliet ◽  
Diana Dorobantu ◽  
Laura Gay
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Brownian Motion ◽  
Monte Carlo Method ◽  
Density Distribution ◽  
Parabolic Cylinder ◽  
Density Distribution Function ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Parabolic Cylinder Functions

AbstractLet X be an Ornstein–Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density / distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this result.

scholarly journals Calculation of Radial Density Distribution Function for main orbital of Carbon atom and Carbon like ions

2014 ◽  
Vol 11 (4) ◽  
pp. 1455-1458
Author(s):  
Baghdad Science Journal
Keyword(s):  
Distribution Function ◽  
Carbon Atom ◽  
Density Distribution ◽  
Computer Software ◽  
Negative Ion ◽  
Radial Density ◽  
Density Distribution Function ◽  
Hartree Fock ◽  
Radial Density Distribution ◽  
Nitrogen Ion

Radial density distribution function of one particle D(r1) was calculated for main orbital of carbon atom and carbon like ions (N+ and B- ) by using the Partitioning technique .The results presented for K and L shells for the Carbon atom and negative ion of Boron and positive ion for nitrogen ion . We observed that as atomic number increases the probability of existence of electrons near the nucleus increases and the maximum of the location r1 decreases. In this research the Hartree-fock wavefunctions have been computed using Mathcad computer software .

scholarly journals On conditional Ornstein–Uhlenbeck processes

1984 ◽  
Vol 16 (04) ◽  
pp. 920-922
Author(s):  
P. Salminen
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Bessel Process ◽  
Uhlenbeck Process ◽  
Brownian Motions ◽  
Ornstein Uhlenbeck Process ◽  
The Law ◽  
Similar Description

It is well known that the law of a Brownian motion started from x > 0 and conditioned never to hit 0 is identical with the law of a three-dimensional Bessel process started from x. Here we show that a similar description is valid for all linear Ornstein–Uhlenbeck Brownian motions. Further, using the same techniques, it is seen that we may construct a non-stationary Ornstein–Uhlenbeck process from a stationary one.

scholarly journals On the Entropy of Fractionally Integrated Gauss–Markov Processes

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2031
Author(s):  
Mario Abundo ◽  
Enrica Pirozzi
Keyword(s):  
Dynamical System ◽  
Stochastic Process ◽  
Brownian Motion ◽  
Markov Process ◽  
Markov Processes ◽  
Numerical Approximation ◽  
Uhlenbeck Process ◽  
Sample Paths ◽  
Ornstein Uhlenbeck Process ◽  
Application Fields

This paper is devoted to the estimation of the entropy of the dynamical system {Xα(t),t≥0}, where the stochastic process Xα(t) consists of the fractional Riemann–Liouville integral of order α∈(0,1) of a Gauss–Markov process. The study is based on a specific algorithm suitably devised in order to perform the simulation of sample paths of such processes and to evaluate the numerical approximation of the entropy. We focus on fractionally integrated Brownian motion and Ornstein–Uhlenbeck process due their main rule in the theory and application fields. Their entropy is specifically estimated by computing its approximation (ApEn). We investigate the relation between the value of α and the complexity degree; we show that the entropy of Xα(t) is a decreasing function of α∈(0,1).

Admission Control for Multidimensional Workload input with Heavy Tails and Fractional Ornstein-Uhlenbeck Process

2015 ◽  
Vol 47 (2) ◽  
pp. 476-505
Author(s):  
Amarjit Budhiraja ◽  
Vladas Pipiras ◽  
Xiaoming Song
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Admission Control ◽  
Control Policy ◽  
Uhlenbeck Process ◽  
Control Policies ◽  
Ornstein Uhlenbeck Process ◽  
Admission Control Policy

The infinite source Poisson arrival model with heavy-tailed workload distributions has attracted much attention, especially in the modeling of data packet traffic in communication networks. In particular, it is well known that under suitable assumptions on the source arrival rate, the centered and scaled cumulative workload input process for the underlying processing system can be approximated by fractional Brownian motion. In many applications one is interested in the stabilization of the work inflow to the system by modifying the net input rate, using an appropriate admission control policy. In this paper we study a natural family of admission control policies which keep the associated scaled cumulative workload input asymptotically close to a prespecified linear trajectory, uniformly over time. Under such admission control policies and with natural assumptions on arrival distributions, suitably scaled and centered cumulative workload input processes are shown to converge weakly in the path space to the solution of a d-dimensional stochastic differential equation driven by a Gaussian process. It is shown that the admission control policy achieves moment stabilization in that the second moment of the solution to the stochastic differential equation (averaged over the d-stations) is bounded uniformly for all times. In one special case of control policies, as time approaches ∞, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H > ½.

scholarly journals Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes

2019 ◽  
Vol 20 (04) ◽  
pp. 2050023 ◽  
Author(s):  
Yong Chen ◽  
Nenghui Kuang ◽  
Ying Li
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Continuous Time ◽  
Index Formula ◽  
Hurst Index ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Observation ◽  
Statistical Estimations ◽  
Drift Parameter

For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index [Formula: see text], we show the Berry–Esséen bound of the least squares estimator of the drift parameter based on the continuous-time observation. We use an approach based on Malliavin calculus given by Kim and Park [Optimal Berry–Esséen bound for statistical estimations and its application to SPDE, J. Multivariate Anal. 155 (2017) 284–304].

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