Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConditions for existence and smoothness of the distribution density for an Ornstein-Uhlenbeck process with Levy noise
294
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Conditions are given, sufficient for the distribution of an Ornstein-Uhlenbeck process with Levy noise to be absolutely continuous or to possess a smooth density. For the processes with non-degenerate drift coefficient, these conditions are a necessary ones. A multidimensional analogue for the non-degeneracy condition on the drift coefficient is introduced.
rate research
Read More
This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent and asymptotically normal in the large-sample limit, using some recent results on the canonical representation and spectral structure of mixed processes.
We study the stochastic growth process in discrete time $x_{i+1} = (1 + mu_i) x_i$ with growth rate $mu_i = rho e^{Z_i - frac12 var(Z_i)}$ proportional to the exponential of an Ornstein-Uhlenbeck (O-U) process $dZ_t = - gamma Z_t dt + sigma dW_t$ sampled on a grid of uniformly spaced times ${t_i}_{i=0}^n$ with time step $tau$. Using large deviation theory methods we compute the asymptotic growth rate (Lyapunov exponent) $lambda = lim_{nto infty} frac{1}{n} log mathbb{E}[x_n]$. We show that this limit exists, under appropriate scaling of the O-U parameters, and can be expressed as the solution of a variational problem. The asymptotic growth rate is related to the thermodynamical pressure of a one-dimensional lattice gas with attractive exponential potentials. For $Z_t$ a stationary O-U process the lattice gas coincides with a system considered previously by Kac and Helfand. We derive upper and lower bounds on $lambda$. In the large mean-reversion limit $gamma n tau gg 1$ the two bounds converge and the growth rate is given by a lattice version of the van der Waals equation of state. The predictions are tested against numerical simulations of the stochastic growth model.
This paper studies Langevin equation with random damping due to multiplicative noise and its solution. Two types of multiplicative noise, namely the dichotomous noise and fractional Gaussian noise are considered. Their solutions are obtained explicitly, with the expressions of the mean and covariance determined explicitly. Properties of the mean and covariance of the Ornstein-Uhlenbeck process with random damping, in particular the asymptotic behavior, are studied. The effect of the multiplicative noise on the stability property of the resulting processes is investigated.
Active Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models include also random noise in particle displacement (Wiener process) resulting in a diffusive motion at short time scales. On the other hand, Ornstein-Uhlenbeck processes consider Langevin dynamics for the particle velocity and predict a motion that is not diffusive at short time scales. However, experiments show that migrating cells may present a varying speed as well as a short-time diffusive behavior. While Ornstein-Uhlenbeck processes can describe the varying speed, Active Mater models can explain the short-time diffusive behavior. Isotropic models cannot explain both: short-time diffusion renders instantaneous velocity ill-defined, hence impeding dynamical equations that consider velocity time-derivatives. On the other hand, both models apply for migrating biological cells and must, in some limit, yield the same observable predictions. Here we propose and analytically solve an Anisotropic Ornstein-Uhlenbeck process that considers polarized particles, with a Langevin dynamics for the particle movement in the polarization direction while following a Wiener process for displacement in the orthogonal direction. Our characterization provides a theoretically robust way to compare movement in dimensionless simulations to movement in dimensionful experiments, besides proposing a procedure to deal with inevitable finite precision effects in experiments or simulations.
In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this simulation, we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process, and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter $H>1/2$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
