Related papers: On the inverse first-passage-time problem for a Wi…

Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit…

Planck formula is considered as a first moment (average value) of unknown function of electromagnetic energy distribution of black body radiation. In-verse problem for the definition of the unknown function is solved for Gibbs ensemble. The…

Let $X$ be a real valued L\'evy process that is in the domain of attraction of a stable law without centering with norming function $c.$ As an analogue of the random walk results in \cite{vw} and \cite{rad} we study the local behaviour of…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…

This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration…

The initial-to-final-state inverse problem consists in determining a quantum Hamiltonian assuming the knowledge of the state of the system at some fixed time, for every initial state. We formulated this problem to establish a theoretical…

We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…

We study the accuracy of a class of methods to compute the Inverse Laplace Transform, the so-called \emph{Abate--Whitt methods} [Abate, Whitt 2006], which are based on a linear combination of evaluations of $\widehat{f}$ in a few points. We…

We present a new approach to the electromagnetic inverse problem that explicitly addresses the ambiguity associated with its ill-posed character. Rather than calculating a single ``best'' solution according to some criterion, our approach…

Inverse scattering aims to infer information about a hidden object by using the received scattered waves and training data collected from forward mathematical models. Recent advances in computing have led to increasing attention towards…

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…

Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…

First passage problems for spectrally negative L\'evy processes with possible absorbtion or/and reflection at boundaries have been widely applied in mathematical finance, risk, queueing, and inventory/storage theory. Historically, such…

Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…

Bayesian optimisation requires fitting a Gaussian process model, which in turn requires specifying prior on the unknown black-box function -- most of the theoretical literature assumes this prior is known. However, it is common to have more…

We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in…

This paper is concerned with the inverse moving source problems for parabolic equations. Given the temporal function, we prove the uniqueness of the nonlinear inverse problem of determining the orbit function by final data measured in a…

Let $X$ be a one-dimensional diffusion and let $g\colon[0,T]\times\mathbb{R}\to\mathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent…