14,994 research outputs found
On the combinatorics of iterated stochastic integrals
This paper derives several identities for the iterated integrals of a general semimartingale. They involve powers, brackets, exponential and the stochastic exponential. Their form and derivations are combinatorial. The formulae simplify for continuous or finite-variation semimartingales, especially for counting processes. The results are motivated by chaotic representation of martingales, and a simple such application is given
Recursion Aware Modeling and Discovery For Hierarchical Software Event Log Analysis (Extended)
This extended paper presents 1) a novel hierarchy and recursion extension to
the process tree model; and 2) the first, recursion aware process model
discovery technique that leverages hierarchical information in event logs,
typically available for software systems. This technique allows us to analyze
the operational processes of software systems under real-life conditions at
multiple levels of granularity. The work can be positioned in-between reverse
engineering and process mining. An implementation of the proposed approach is
available as a ProM plugin. Experimental results based on real-life (software)
event logs demonstrate the feasibility and usefulness of the approach and show
the huge potential to speed up discovery by exploiting the available hierarchy.Comment: Extended version (14 pages total) of the paper Recursion Aware
Modeling and Discovery For Hierarchical Software Event Log Analysis. This
Technical Report version includes the guarantee proofs for the proposed
discovery algorithm
Appell polynomials and their relatives
This paper summarizes some known results about Appell polynomials and
investigates their various analogs. The primary of these are the free Appell
polynomials. In the multivariate case, they can be considered as natural
analogs of the Appell polynomials among polynomials in non-commuting variables.
They also fit well into the framework of free probability. For the free Appell
polynomials, a number of combinatorial and "diagram" formulas are proven, such
as the formulas for their linearization coefficients. An explicit formula for
their generating function is obtained. These polynomials are also martingales
for free Levy processes. For more general free Sheffer families, a necessary
condition for pseudo-orthogonality is given. Another family investigated are
the Kailath-Segall polynomials. These are multivariate polynomials, which share
with the Appell polynomials nice combinatorial properties, but are always
orthogonal. Their origins lie in the Fock space representations, or in the
theory of multiple stochastic integrals. Diagram formulas are proven for these
polynomials as well, even in the q-deformed case.Comment: 45 pages, 2 postscript figure
Timed Multiparty Session Types
We propose a typing theory, based on multiparty session types, for modular verification of real-time choreographic interactions. To model real-time implementations, we introduce a simple calculus with delays and a decidable static proof system. The proof system ensures type safety and time-error freedom, namely processes respect the prescribed timing and causalities between interactions. A decidable condition on timed global types guarantees time-progress for validated processes with delays, and gives a sound and complete characterisation of a new class of CTAs with general topologies that enjoys progress and liveness
Majority dynamics on trees and the dynamic cavity method
A voter sits on each vertex of an infinite tree of degree , and has to
decide between two alternative opinions. At each time step, each voter switches
to the opinion of the majority of her neighbors. We analyze this majority
process when opinions are initialized to independent and identically
distributed random variables. In particular, we bound the threshold value of
the initial bias such that the process converges to consensus. In order to
prove an upper bound, we characterize the process of a single node in the large
-limit. This approach is inspired by the theory of mean field spin-glass and
can potentially be generalized to a wider class of models. We also derive a
lower bound that is nontrivial for small, odd values of .Comment: Published in at http://dx.doi.org/10.1214/10-AAP729 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Consumption processes and positively homogeneous projection properties
We constructively prove the existence of time-discrete consumption processes
for stochastic money accounts that fulfill a pre-specified positively
homogeneous projection property (PHPP) and let the account always be positive
and exactly zero at the end. One possible example is consumption rates forming
a martingale under the above restrictions. For finite spaces, it is shown that
any strictly positive consumption strategy with restrictions as above possesses
at least one corresponding PHPP and could be constructed from it. We also
consider numeric examples under time-discrete and -continuous account
processes, cases with infinite time horizons and applications to income
drawdown and bonus theory.Comment: 24 pages, 2 figure
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