L\'evy-Schr\"odinger wave packets

We analyze the time--dependent solutions of the pseudo--differential L\'evy--Schr\"odinger wave equation in the free case, and we compare them with the associated L\'evy processes. We list the principal laws used to describe the time evolutions of both the L\'evy process densities, and the L\'evy--Schr\"odinger wave packets. To have self--adjoint generators and unitary evolutions we will consider only absolutely continuous, infinitely divisible L\'evy noises with laws symmetric under change of sign of the independent variable. We then show several examples of the characteristic behavior of the L\'evy--Schr\"odinger wave packets, and in particular of the bi-modality arising in their evolutions: a feature at variance with the typical diffusive uni--modality of both the L\'evy process densities, and the usual Schr\"odinger wave functions.Comment: 41 pages, 13 figures; paper substantially shortened, while keeping intact examples and results; changed format from "report" to "article"; eliminated Appendices B, C, F (old names); shifted Chapters 4 and 5 (old numbers) from text to Appendices C, D (new names); introduced connection between Relativistic q.m. laws and Generalized Hyperbolic law

On Uniqueness of the Jump Process in Quantum Measurement Theory

We prove that, contrary to the standard quantum theory of continuous observation, in the formalism of Event Enhanced Quantum Theory the stochastic process generating individual sample histories of pairs (observed quantum system, observing classical apparatus) is unique. This result gives a rigorous basis to the previous heuristic argument of Blanchard and Jadczyk. Possible implications of this result are discussed.Comment: 31 pages, LaTeX, article; e-mail contact [email protected]

ARBITRAGE AND FREE LUNCH WITH BOUNDED RISK FOR UNBOUNDED CONTINUOUS PROCESSES

We give two examples showing that for unbounded continuous price processes, the no-free-lunch assumption and the existence of an equivalent martingale measure are not equivalent. In fact it turns out that the notion of an equivalent local martingale measure is natural in this context. Copyright 1994 Blackwell Publishers.