Related papers: A hyperbolastic type-I diffusion process: Paramete…
We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the…
There has been recent work [Louis STOC 2015] to analyze the spectral properties of hypergraphs with respect to edge expansion. In particular, a diffusion process is defined on a hypergraph such that within each hyperedge, measure flows from…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…
This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…
Accurately quantifying air-sea fluxes is important for understanding air-sea interactions and improving coupled weather and climate systems. This study introduces a probabilistic framework to represent the highly variable nature of air-sea…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…
In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially…
This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…
Firefly algorithms belong to modern meta-heuristic algorithms inspired by nature that can be successfully applied to continuous optimization problems. In this paper, we have been applied the firefly algorithm, hybridized with local search…
We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…
In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
We study structural equation modeling (SEM) for diffusion processes with jumps. Based on high-frequency data, we consider the parameter estimation and the goodness-of-fit test in the SEM. Using a threshold method, we propose the…
Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian…
In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…
We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…