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We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the…
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…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We consider the problem of detecting an abrupt change in the distribution of a sequentially observed stochastic process. We establish the optimality of the CUSUM test with respect to a modified version of Lorden's criterion for arbitrary…
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation…
We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals.…
The self-similar asymptotics for solutions to the drift-diffusion equation with fractional dissipation, coupled to the Poisson equation, is analyzed in the whole space. It is shown that in the subcritical and supercritical cases, the…
The presented paper tackles the problem of modeling an unknown function, and its first $r-1$ derivatives, out of scattered and poor-quality data. The considered setting embraces a large number of use cases addressed in the literature and…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…