Discretization error for a two-sided reflected Lévy process

An obvious way to simulate a Lévy process X is to sample its increments over time 1 / n, thus constructing an approximating random walk \(X^{(n)}\). This paper considers the error of such approximation after the two-sided reflection map is applied, with focus on the value of the resulting process Y and regulators L, U at the lower and upper barriers at some fixed time. Under the weak assumption that \(X_\varepsilon /a_\varepsilon \) has a non-trivial weak limit for some scaling function \(a_\varepsilon \) as \(\varepsilon \downarrow 0\), it is proved in particular that \((Y_1-Y^{(n)}_n)/a_{1/n}\) converges weakly to \(\pm \, V\), where the sign depends on the last barrier visited. Here the limit V is the same as in the problem concerning approximation of the supremum as recently described by Ivanovs (Ann Appl Probab, 2018). Some further insight in the distribution of V is provided both theoretically and numerically.     

Mechanism of the Palladium‐Catalyzed Synthesis of Münchnones: The Role of Ligands in N‐Acyl Iminium Salt Carbonylation

The palladium‐catalyzed carbonylative coupling of imines, acid chlorides, and dipolarophiles can provide efficient routes to prepare nitrogen‐containing heterocycles. One challenge in developing this reaction, and in the creation of more active catalyst systems, is the lack of data on how this complex transformation proceeds. To address this, we report here the results of our mechanistic studies on this system, and in particular the formation of mesoionic münchnones. This includes the synthesis of key catalytic intermediates, model reactions, and kinetic studies that support the role of these compounds in catalysis. Together, these studies provide a clear picture of the impact of catalyst structure, ligands, and palladium nanoparticles on facilitating the carbonylation of in situ generated iminium salts, and suggest an avenue for the creation of more active catalyst systems.     

First passage of time-reversible spectrally negative Markov additive processes

We study the first passage process of a spectrally negative Markov additive process (MAP). The focus is on the background Markov chain at the times of the first passage. This process is a Markov chain itself with a transition rate matrix Λ. Assuming time reversibility, we show that all the eigenvalues of Λ are real, with algebraic and geometric multiplicities being the same, which allows us to identify the Jordan normal form of Λ. Furthermore, this fact simplifies the analysis of fluctuations of a MAP. We provide an illustrative example and show that our findings greatly reduce the computational efforts required to obtain Λ in the time-reversible case.     

Singularities of the matrix exponent of a Markov additive process with one-sided jumps

We analyze the number of zeros of det(F(α))$det\left(F\left(\alpha \right)\right)$, where F(α)$F\left(\alpha \right)$ is the matrix exponent of a Markov Additive Process (MAP) with one-sided jumps. The focus is on the number of zeros in the right half of the complex plane, where F(α)$F\left(\alpha \right)$ is analytic. In addition, we also consider the case of a MAP killed at an independent exponential time. The corresponding zeros can be seen as the roots of a generalized Cramér–Lundberg equation. We argue that our results are particularly useful in fluctuation theory for MAPs, which leads to numerous applications in queueing theory and finance.     

Novel Copolymers of Styrene. 11. Ring-Substituted 2-Cyano-3-phenyl-2-propenamides

Novel electrophilic trisubstituted ethylene monomers, halo ring-disubstituted 2-cyano-3-phenyl-2-propenamides, RPhCH = C(CN)CONH₂, where R is 2,3-difluoro, 2,4-difluoro, 2,5-difluoro, 2,6-difluoro, 3,4-difluoro, 3,5-difluoro, 2-chloro-4-fluoro, 3-chloro-2-fluoro, 3-chloro-4-fluoro were prepared and copolymerized with styrene. The monomers were synthesized by potassium hydroxide catalyzed Knoevenagel condensation of ring-substituted benzaldehydes and cyanoacetamide, and characterized by CHN elemental analysis, IR, ¹H- and ¹³C-NMR. Novel copolymers of the ethylenes and styrene were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator, ABCN at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H- and ¹³C-NMR, GPC, DSC, and TGA. High T_g of the copolymers in comparison with that of polystyrene indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. Decomposition of the copolymers in nitrogen occurred in two steps, first in the 200–500°C range with residue (10–14 wt%), which then decomposed in the 500–800°C range.     

Another look into decomposition results

In this note, we identify a simple setup from which one may easily infer various decomposition results for queues with interruptions as well as càdlàg processes with certain secondary jump inputs. Special cases are processes with stationary or stationary and independent increments. In the Lévy process case, the decomposition holds not only in the limit but also at independent exponential times, due to the Wiener–Hopf decomposition. A similar statement holds regarding the GI/GI/1 setting with multiple vacations.     

The Tax Identity For Markov Additive Risk Processes

Taxed risk processes, i.e. processes which change their drift when reaching new maxima, represent a certain type of generalizations of Lévy and of Markov additive processes (MAP), since the times at which their Markovian mechanism changes are allowed to depend on the current position. In this paper we study generalizations of the tax identity of Albrecher and Hipp (2007) from the classical risk model to more general risk processes driven by spectrally-negative MAPs. We use the Sparre Andersen risk processes with phase-type interarrivals to illustrate the ideas in their simplest form.