Related papers: Approximation and estimation of scale functions fo…
Randomly scaled scale-decorated Poisson point process is introduced recently in Bhattacharya et al. [2017] where it appeared as weak limit of a sequence of point processes in the context of branching random walk. In this article, we obtain…
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative L\'evy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This…
In this paper we solve the exit problems for (reflected) spectrally negative L\'evy processes, which are exponentially killed with a killing intensity dependent on the present state of the process and analyze respective resolvents. All…
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…
Uniform asymptotic expansions involving exponential and Airy functions are obtained for Laguerre polynomials $L_{n}^{(\alpha)}(x)$, as well as complementary confluent hypergeometric functions. The expansions are valid for $n$ large and…
This article deals with adaptive nonparametric estimation for L\'evy processes observed at low frequency. For general linear functionals of the L\'evy measure, we construct kernel estimators, provide upper risk bounds and derive rates of…
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to…
Laguerre polynomials are orthogonal polynomials defined on positive half line with respect to weight $e^{-x}$. They have wide applications in scientific and engineering computations. However, the exponential growth of Laguerre polynomials…
We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a…
This paper considers discretization of the L\'evy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity…
It is important to estimate the errors of probabilistic inference algorithms. Existing diagnostics for Markov chain Monte Carlo methods assume inference is asymptotically exact, and are not appropriate for approximate methods like…
In the paper we consider the problem of multivariate function approximation in polynomial basis. In order to solve this problem, we adjust the least squares method (LSM) by adding information about derivatives of the function. This…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear,…
Tempered fractional derivatives originated from the tempered fractional diffusion equations (TFDEs) modeled on the whole space R (see [23]). For numerically solving TFDEs, two kinds of generalized Laguerre functions were defined and some…
We develop new representations for the Levy measures of the beta and gamma processes. These representations are manifested in terms of an infinite sum of well-behaved (proper) beta and gamma distributions. Further, we demonstrate how these…
We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive L\'evy processes. Via Lamperti type transforms, these results can be applied to obtain new integral tests on extinction…
Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…