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In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
In this work, we explore a numerical approach for performing the inverse Laplace transformation, with an emphasis on achieving stability and robustness under noisy conditions. Our quadrature-based method integrates reparameterization, data…
Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai…
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical representations, where the integer appears as an explicit…
Bayesian inference tasks continue to pose a computational challenge. This especially holds for spatial-temporal modeling where high-dimensional latent parameter spaces are ubiquitous. The methodology of integrated nested Laplace…
A formula of Doetsch ({\em Math. Zeitschr.} {\bf 42}, 263 (1937)) is generalized and used to numerically invert the one-sided Laplace transform ${\hat C}(\beta)$. The necessary input is only the values of ${\hat C}(\beta)$ on the positive…
In this paper we consider a dynamic computer simulator that produces a time-series response $y_t(x)$ over $L$ time points, for every given input parameter $x$. We propose a method for solving inverse problems, which refer to the finding of…
We propose the first method that realizes the Laplace mechanism exactly (i.e., a Laplace noise is added to the data) that requires only a finite amount of communication (whereas the original Laplace mechanism requires the transmission of a…
This paper examines the noise handling properties of three of the most widely used algorithms for numerically inverting the Laplace Transform. After examining the genesis of the algorithms, the regularization properties are evaluated…
The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the…
We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on $\mathbb Z$ (that is, including both negative and positive integers). Our…
A time integration scheme based on the Laplace Transform (LT) has been implemented in a baroclinic primitive equation model. The LT scheme provides an attractive alternative to the popular semi-implicit (SI) scheme. Analysis shows that it…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…