Related papers: A simple mathematical model for anomalous diffusio…
We provide a Lyapunov convergence analysis for time-inhomogeneous variable coefficient stochastic differential equations (SDEs). Three typical examples include overdamped, irreversible drift, and underdamped Langevin dynamics. We first…
Anomalous subdiffusion characterizes transport in diverse physical systems and is especially prevalent inside biological cells. In cell biology, the prevailing model for chemical activation rates has recently changed from the first passage…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
We propose an information-theoretic alternative to the popular Cronbach alpha coefficient of reliability. Particularly suitable for contexts in which instruments are scored on a strictly nonnumeric scale, our proposed index is based on…
Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…
A straightforward analytical scheme is proposed for computing the long-time, asymptotic mean velocity and dispersivity (effective diffusivity) of a particle undergoing a discrete biased random walk on a periodic lattice amongst an array of…
We consider non-linear regression models corrupted by generic noise when the regression functions form a non-linear subspace of L^2, relevant in non-linear PDE inverse problems and data assimilation. We show that when the score of the model…
The frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency independent…
In this work, we propose some numerical schemes for linear kinetic equations in the diffusion and anomalous diffusion limit. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate…
We present a Master Equation formulation based on a Markovian random walk model that exhibits sub-diffusion, classical diffusion and super-diffusion as a function of a single parameter. The non-classical diffusive behavior is generated by…
We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the literature by allowing one to completely dispense from…
In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…
As well known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus attention on some new aspects of the…
Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…
We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] + D\partial^2_x \rho^\nu$, where the potential of the drift, $U(x)$, presents a…
For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting…
We consider the processing of statistical samples $X\sim P_\theta$ by a channel $p(y|x)$, and characterize how the statistical information from the samples for estimating the parameter $\theta\in\mathbb{R}^d$ can scale with the mutual…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…