Alexey Kuznetsov

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In this paper we introduce a ten-parameter family of Lévy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes similar to the generalized tempered stable, KoBoL and CGMY processes. Analytically it is characterized by(More)
The purpose of this review article is to give an up to date account of the theory and applications of scale functions for spectrally negative Lévy processes. Our review also includes the first extensive overview of how to work numerically with scale functions. Aside from being well acquainted with the general theory of probability, the reader is assumed to(More)
In this article we consider some increasing trees, the number of which is equal to the number of alternating (updown) permutations, that is, permutations of the form σ(1) < σ(2) > σ(3) < ... . It turns out that there are several such classes of increasing trees, each of which is interesting in itself. Special attention is paid to the study of various(More)
The search for a canonical set of eigenvectors of the discrete Fourier transform has been ongoing for more than three decades. The goal is to find an orthogonal basis of eigenvectors which would approximate Hermite functions – the eigenfunctions of the continuous Fourier transform. This eigenbasis should also have some degree of analytical tractability and(More)
Oscillatory regulatory networks have been discovered in many cellular pathways. An especially challenging area is studying dynamics of cellular oscillators interacting with one another in a population. Synchronization is only one of and the simplest outcome of such interaction. It is suggested that the outcome depends on the structure of the network.(More)
In this talk, I will discuss Hankel determinant generated by a Laguerre weight multiplied by exp(−t/x), t > 0, inducing an infinitely fast 0 at the origin. For finite n, the Hankel determinant, is expressed in terms a finite n Painleve III. Under double scaling where n→∞ and t→ 0, such that s := 2nt is finite, the original PIII becomes a lesser PIII. The(More)
Various 2-substituted indolizines can be directly and selectively lithiated in the 5 position and subsequent reactions with different electrophiles lead to some novel classes of indolizines. In particular, previously unknown 5-formyl- and 5-iodoindolizine have been prepared by this way and the molecular structure of 5-formyl-2- phenylindolizine was(More)
We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series representations for the characteristic function and for the density of a free stable distribution. All of these formulas bear close(More)