1,595 research outputs found
Conditioned Martingales
It is well known that upward conditioned Brownian motion is a
three-dimensional Bessel process, and that a downward conditioned Bessel
process is a Brownian motion. We give a simple proof for this result, which
generalizes to any continuous local martingale and clarifies the role of finite
versus infinite time in this setting. As a consequence, we can describe the law
of regular diffusions that are conditioned upward or downward.Comment: Corrected several typos, improved formulations. Accepted by
Electronic Communications in Probability; Electronic Communications in
Probability, 2012, Volume 17, Issue 4
Fault testing quantum switching circuits
Test pattern generation is an electronic design automation tool that attempts
to find an input (or test) sequence that, when applied to a digital circuit,
enables one to distinguish between the correct circuit behavior and the faulty
behavior caused by particular faults. The effectiveness of this classical
method is measured by the fault coverage achieved for the fault model and the
number of generated vectors, which should be directly proportional to test
application time. This work address the quantum process validation problem by
considering the quantum mechanical adaptation of test pattern generation
methods used to test classical circuits. We found that quantum mechanics allows
one to execute multiple test vectors concurrently, making each gate realized in
the process act on a complete set of characteristic states in space/time
complexity that breaks classical testability lower bounds.Comment: (almost) Forgotten rewrite from 200
Pathwise stochastic integrals for model free finance
We present two different approaches to stochastic integration in frictionless
model free financial mathematics. The first one is in the spirit of It\^o's
integral and based on a certain topology which is induced by the outer measure
corresponding to the minimal superhedging price. The second one is based on the
controlled rough path integral. We prove that every "typical price path" has a
naturally associated It\^o rough path, and justify the application of the
controlled rough path integral in finance by showing that it is the limit of
non-anticipating Riemann sums, a new result in itself. Compared to the first
approach, rough paths have the disadvantage of severely restricting the space
of integrands, but the advantage of being a Banach space theory. Both
approaches are based entirely on financial arguments and do not require any
probabilistic structure.Comment: Published at http://dx.doi.org/10.3150/15-BEJ735 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Supermartingales as Radon-Nikodym densities and related measure extensions
Certain countably and finitely additive measures can be associated to a given
nonnegative supermartingale. Under weak assumptions on the underlying
probability space, existence and (non)uniqueness results for such measures are
proven.Comment: Published at http://dx.doi.org/10.1214/14-AOP956 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Improved Quantum Cost for n-bit Toffoli Gates
We present an n-bit Toffoli gate quantum circuit based on the realization
proposed by Barenco, where some of the Toffoli gates in their construction are
replaced with Peres gates. This results in a significant cost reduction. Our
main contribution is a quantum circuit which simulates the (m+1)-bit Toffoli
gate with 32m-96 elementary quantum gates and one garbage bit which is passed
unchanged. This paper is a corrected and expanded version of our recent journal
publication
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