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A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H.. van
On the other hand, Feller’s branching diffusion is a special case of the general continuous state branching processes (CSBP’s) initially studied by Jiˇrina [19], Lamperti [22, 23],
The boundary dimension of B [0 , 1] is the Hausdorff dimension of the “frontier” of Brownian motion, where the frontier of planar Brownian motion is t he boundary of the un-
Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and
the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2..
(2) Branching Mechanism Reconstruction: By reconstruction of the branching mech- anism, the variable coefficient σ ( x ) of the branching generator is transformed as a
In an earlier paper [4] by the first author, the random motion of a rigid body is studied using a stochastic differential equation on the rotation group SO(3) driven by a
The branching property can be summarised into the fact that given her type and birth time, the daughter process of any individual born is independent of all individuals not in
