Related papers: Laplace Transforms of Improper Random Variables

Lyapunov exponents (LEs) are key indicators of chaos in dynamical systems. In general relativity the classical definition of LE meets difficulty because it is not coordinate invariant and spacetime coordinates lose their physical meaning as…

In ref [math.ST/0411462] the notion of statistically dual distributions is introduced. The reconstruction of confidence density [AIP Conference Proceedings 803 (2005) 398] for the location parameter for several pairs of statistically dual…

Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to…

We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized…

This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden…

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent L\'evy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but…

This note aims to verify a Laplace transform pair, previously published without proof, concerning the expected stock-out that may occur in a production-inventory systems when demand is Poisson, and the time horizon is finite. Stock-out, or…

It is proved that the classical Laplace transform is a continuous valuation which is positively GL$(n)$ covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform.

Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…

We construct intrinsic on-and off-diagonal upper and lower estimates for the transition probability density of a L\'evy process in small time. By intrinsic we mean that such estimates reflect the structure of the characteristic exponent of…

In this paper we find the Laplace transforms of the weighted occupation times for a spectrally negative L\'evy surplus process to spend below its running maximum up to the first exit times. The results are expressed in terms of generalized…

We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness…

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…

A sequence of large invertible matrices given by a small random perturbation around a fixed diagonal and positive matrix induces a random dynamics on a high-dimensional sphere. For a certain class of rotationally invariant random…

Machine learning models have undeniably achieved impressive performance across a range of applications. However, their often perceived black-box nature, and lack of transparency in decision-making, have raised concerns about understanding…

In this short note, we present few results on the use of the discrete Laplace transform in solving first and second order initial value problems of discrete differential equations.

Transformation models are a very important tool for applied statisticians and econometricians. In many applications, the dependent variable is transformed so that homogeneity or normal distribution of the error holds. In this paper, we…

A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…

This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…