Related papers: Path Decomposition of Spectrally Negative Levy Pro…

In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This…

We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold.…

We present an exact sampling method for the first passage event of a Levy process. The idea is to embed the process into another one whose first passage event can be sampled exactly, and then recover the part belonging to the former from…

For a refracted L\'evy process driven by a spectrally negative L\'evy process, we use a different approach to derive expressions for its q-potential measures without killing. Unlike previous methods whose derivations depend on scale…

In this paper, we analyze some distributions involving the longest and shortest negative excursions of spectrally negative L\'evy processes using the binomial expansion approach. More specifically, we study the distributions of such…

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…

We give conditions under which the tail probability of the supremum over unit interval of a Levy process with light tail is equivalent to the tail of the value of the process at the right endpoint.

We revisit a stochastic control problem of optimally modifying the underlying spectrally negative Levy process. A strategy must be absolutely continuous with respect to the Lebesgue measure, and the objective is to minimize the total costs…

In this note we find a formula for the supremum distribution of spectrally positive or negative L\'evy processes with a broken linear drift. This gives formulas for ruin probabilities in the case when two insurance companies (or two…

We present a new family of graphs with remarkable properties. They are obtained by connecting the points of a random walk when their distance is smaller than a given scale. Their degree (number of neighbors) does not depend on the graph's…

We present a new and easy-to-implement sequential sampling method for CGMY processes with either finite or infinite variation, exploiting the time change representation of the CGMY model and a decomposition of its time change. We find that…

Enhancing low-light traffic images is crucial for reliable perception in autonomous driving, intelligent transportation, and urban surveillance systems. Nighttime and dimly lit traffic scenes often suffer from poor visibility due to low…

We consider a problem of localizing a path-signal that evolves over time on a graph. A path-signal can be viewed as the trajectory of a moving agent on a graph in several consecutive time points. Combining dynamic programming and graph…

Only phase space is typically used to obtain final state particle spectra in rare decay searches, which is a crude approximation in the case of three body processes. We will demonstrate how both dynamics and phase space can be approximately…

We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…

Distributional identities for a L\'evy process $X_t$, its quadratic variation process $V_t$ and its maximal jump processes, are derived, and used to make "small time" (as $t\downarrow0$) asymptotic comparisons between them. The…

We study the a.s. sample path regularity of Gaussian processes. To this end we relate the path regularity directly to the theory of small deviations. In particular, we show that if the process is $n$-times differentiable then the…

Filterless optical transport networks relies on passive optical interconnections between nodes, i.e., on splitters/couplers and amplifiers. While different studies have investigated their design, none of them offer a solution for an optimal…

Levy flights and subdiffusive processes and their properties are discussed. We derive the space- and time-fractional transport equations, and consider their solutions in external potentials. An extensive list of references is included.

The paper presents a novel model order reduction technique for large-scale linear parameter varying (LPV) systems. The approach is based on decoupling the original dynamics into smaller dimensional LPV subsystems that can be independently…