Related papers: Weak-consistent dynamic correlation estimators for…
This analysis derives the maximum likelihood estimator and applies Bayesian inference to model geometric Brownian motion, incorporating jump diffusion to account for sudden market shifts. The Bayesian approach is implemented using Markov…
Nuclear magnetic resonance (NMR) is sensitive to dynamics on a wide range of correlation times. Recently, we have shown that analysis of relaxation rates via fitting to a correlation function with a small number of exponential terms could…
Motions of fluctuating Brownian particles in an incompressible viscous fluid have been studied by coupled simulations of Brownian particles and host fluid. We calculated the velocity autocorrelation functions of Brownian particles and…
It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter $d$ converges weakly to fractional Brownian motion for $d>1/2$. We show that, for any non-negative integer $M$,…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…
Dynamical aspects of quantum Brownian motion in a low temperature environment are investigated. We give a systematic calculation of quantum entanglement among two Brownian oscillators without invoking Born-Markov approximation widely used…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
We consider the dynamics of a microswimmer and show that they can be approximated by active Brownian motion. The swimmer is modeled by coupled overdamped Langevin equations with periodic driving. We compare the energy dissipation of the…
A Brownian motion model is devised on the manifold of S-matrices, and applied to the calculation of conductance-conductance correlations and of the weak localization peak. The model predicts that (i) the correlation function in $B$ has the…
We present a duality relation between two systems of coalescing random walks and an analogous duality relation between two systems of coalescing Brownian motions. Our results extends previous work in the literature and we apply it to the…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
We define a generalized index of jump activity, propose estimators of that index for a discretely sampled process and derive the estimators' properties. These estimators are applicable despite the presence of Brownian volatility in the…
We introduce a Predictor-Corrector type method suitable for performing many-particle Brownian Dynamics simulations. Since the method goes over to the Gear's method for Molecular Dynamics simulation in the limit of vanishing friction, we…
We study dynamical correlations of two coupled large spins depending on the time and on the spin quantum numbers. In the high-temperature approximation, we obtain analytical expressions for the mutual informations, quantum and classical…
The well-known reflection coupling gives a maximal coupling of two one-dimensional Brownian motions with different starting points. Nevertheless, the reflection coupling does not generalize to more than two Brownian motions. In this paper,…
We construct a non-Markovian coupling for hypoelliptic diffusions which are Brownian motions in the three-dimensional Heisenberg group. We then derive properties of this coupling such as estimates on the coupling rate, and upper and lower…
The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a…
High frequency based estimation methods for a semiparametric pure-jump subordinated Brownian motion exposed to a small additive microstructure noise are developed building on the two-scales realized variations approach originally developed…
We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…
The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…