Simple examples of pure-jump strict local martingales

We present simple new examples of pure-jump strict local martingales. The examples are constructed as exponentials of self-exciting affine Markov processes. We characterize the strict local martingale property of these processes by an integral criterion and by non-uniqueness of an associated ordinary differential equation. Finally we show an alternative construction for our examples by an absolutely continuous measure change in the spirit of (Delbaen and Schachermayer, PTRF 1995)

Sequence motifs that distinguish ATP(CTP) : tRNA nucleotidyl transferases from eubacterial poly(A) polymerases

ATP(CTP):tRNA nucleotidyl transferases, tRNA maturing enzymes found in all organisms, and eubacterial poly(A) polymerases, enzymes involved in mRNA degradation, are so similar that until now their biochemical functions could not be distinguished by their amino acid sequence. BLAST searches and analysis with the program "Sequence Space" for the prediction of functional residues revealed sequence motifs which define these two protein families. One of the poly(A) polymerase defining motifs specifies a structure that we propose to function in binding the 3' terminus of the RNA substrate. Similar motifs are found in other homopolyribonucleotidyl transferases. Phylogenetic classification of nucleotidyl tranferases from sequenced genomes reveals that eubacterial poly(A) polymerases have evolved relatively recently and are found only in a small group of bacteria and surprisingly also in plants, where they may function in organelles