## 10 Citations

### Statistics for diffusion processes with low and high-frequency observations

- Mathematics
- 2016

In this thesis, we consider the problem of nonparametric estimation of the diffusion coefficients of a scalar time-homogeneous Itô diffusion process from discrete observations under various sampling…

### Low-rank diffusion matrix estimation for high-dimensional time-changed Lévy processes

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2018

The estimation of the diffusion matrix $\Sigma$ of a high-dimensional, possibly time-changed L\'evy process is studied, based on discrete observations of the process with a fixed distance. A low-rank…

### Adaptive invariant density estimation for ergodic diffusions over anisotropic classes

- MathematicsThe Annals of Statistics
- 2018

Consider some multivariate diffusion process X = (Xt)t≥0 with unique invariant probability measure and associated invariant density ρ, and assume that a continuous record of observations X =…

### Spectral thresholding for the estimation of Markov chain transition operators

- MathematicsElectronic Journal of Statistics
- 2021

We consider nonparametric estimation of the transition operator $P$ of a Markov chain and its transition density $p$ where the singular values of $P$ are assumed to decay exponentially fast. This is…

### Inheritance of strong mixing and weak dependence under renewal sampling

- MathematicsJournal of Applied Probability
- 2022

Let X be a continuous-time strongly mixing or weakly dependent process and let T be a renewal process independent of X. We show general conditions under which the sampled process
…

### Statistical inference in high-dimensional matrix models

- Mathematics, Computer Science
- 2020

This thesis exemplarily considers three matrix models, matrix completion, Principal Component Analysis (PCA) with Gaussian data and transition operators of Markov chains, and investigates the existence of adaptive confidence sets in the ’Bernoulli’ and ’trace-regression’ models.

### Consistency of nonparametric Bayesian methods for two statistical inverse problems arising from partial differential equations

- Mathematics
- 2020

Supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis

### Nonparametric volatility estimation in scalar diffusions: Optimality across observation frequencies

- MathematicsBernoulli
- 2018

The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the…

### Scale invariant volatility estimation in scalar diffusions

- Mathematics
- 2015

We study nonparametric volatility estimation of a scalar diffusion process observed at equidistant time points. We use the spectral representation of the volatility in terms of the invariant density…

### Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift

- Mathematics
- 2014

As a starting point we prove a functional central limit theorem for estimators of the invariant measure of a geometrically ergodic Harris-recurrent Markov chain in a multi-scale space. This allows to…

## References

SHOWING 1-10 OF 34 REFERENCES

### Nonparametric estimation of scalar diffusions based on low frequency data

- Mathematics
- 2002

We study the problem of estimating the coefficients of a diffusion (X t , t ≥ 0); the estimation is based on discrete data X n Δ, n = 0, 1,..., N. The sampling frequency Δ -1 is constant, and…

### Estimators of diffusions with randomly spaced discrete observations: A general theory

- Mathematics
- 2004

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time…

### The Effects of Random and Discrete Sampling When Estimating Continuous-Time Diffusions

- Mathematics
- 2002

High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data…

### Stochastic Population Theory: Diffusion Processes

- Mathematics
- 1986

In the previous contribution we discussed birth and death processes as models of populations subject to random growth. There, the population size at each instant was represented as a discrete random…

### Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions

- Mathematics
- 2015

We consider nonparametric Bayesian inference in a reflected diffusion model $dX_t = b (X_t)dt + \sigma(X_t) dW_t,$ with discretely sampled observations $X_0, X_\Delta, \dots, X_{n\Delta}$. We analyse…

### A tail inequality for suprema of unbounded empirical processes with applications to Markov chains

- Mathematics
- 2007

We present a tail inequality for suprema of empirical processes generated by variables with finite $\psi_\alpha$ norms and apply it to some geometrically ergodic Markov chains to derive similar…

### Principal Components and Long Run Implications of Multivariate Diffusions

- Mathematics
- 2009

We investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but we allow for a general…

### Econometrics of Diffusion Models

- Economics, Mathematics
- 2010

We review some of the econometric and statistical methods available to estimate and test continuous-time diffusion models from discrete observations, with a particular emphasis on likelihood methods.…