Related papers: Quantile estimation for L\'evy measures
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
We study the quantum walk subjected to measurements with a L\'evy waiting-time distribution. We find that the system has a sub-ballistic behavior instead of a diffusive one. We obtain an analytical expression for the exponent of the power…
These lectures notes aim at introducing L\'{e}vy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of L\'{e}vy processes. We analyze a `toy' example of a…
In this paper, adaptive estimation based on noisy quantized observations is studied. A low complexity adaptive algorithm using a quantizer with adjustable input gain and offset is presented. Three possible scalar models for the parameter to…
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…
In this paper, local linear estimators are adapted for the unknown infinitesimal coefficients associated with continuous-time asset return model with jumps, which can correct the bias automatically due to their simple bias representation.…
We consider the problem of locating a jump discontinuity (change-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding…
Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…
We study jump-diffusion processes with parameters switching at random times. Being motivated by possible applications, we characterise equivalent martingale measures for these processes by means of the relative entropy. The minimal entropy…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the L\'evy processes and is able to realistically reproduce the jump-type…
This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental…
We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…
Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate L\'evy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting…
The histories-based framework of Quantum Measure Theory assigns a generalized probability or measure $\mu(E)$ to every (suitably regular) set $E$ of histories. Even though $\mu(E)$ cannot in general be interpreted as the expectation value…
We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and…
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged…