641 research outputs found
Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3
We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius
number. For the case of symmetric semigroups with three generators of Frobenius
numbers we found an exact formula, which in a sense is the sum of two
Sylvester's formulaes. We prove that the fraction of the symmetric semigroups
is vanishing in the weak limit
Skew convolution semigroups and affine Markov processes
A general affine Markov semigroup is formulated as the convolution of a
homogeneous one with a skew convolution semigroup. We provide some sufficient
conditions for the regularities of the homogeneous affine semigroup and the
skew convolution semigroup. The corresponding affine Markov process is
constructed as the strong solution of a system of stochastic equations with
non-Lipschitz coefficients and Poisson-type integrals over some random sets.
Based on this characterization, it is proved that the affine process arises
naturally in a limit theorem for the difference of a pair of reactant processes
in a catalytic branching system with immigration.Comment: Published at http://dx.doi.org/10.1214/009117905000000747 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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