2,683 research outputs found
A Stochastic Broadcast Pi-Calculus
In this paper we propose a stochastic broadcast PI-calculus which can be used
to model server-client based systems where synchronization is always governed
by only one participant. Therefore, there is no need to determine the joint
synchronization rates. We also take immediate transitions into account which is
useful to model behaviors with no impact on the temporal properties of a
system. Since immediate transitions may introduce non-determinism, we will show
how these non-determinism can be resolved, and as result a valid CTMC will be
obtained finally. Also some practical examples are given to show the
application of this calculus.Comment: In Proceedings QAPL 2011, arXiv:1107.074
Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation
The "correlated-projection technique" has been successfully applied to derive
a large class of highly non Markovian dynamics, the so called non Markovian
generalized Lindblad type equations or Lindblad rate equations. In this
article, general unravellings are presented for these equations, described in
terms of jump-diffusion stochastic differential equations for wave functions.
We show also that the proposed unravelling can be interpreted in terms of
measurements continuous in time, but with some conceptual restrictions. The
main point in the measurement interpretation is that the structure itself of
the underlying mathematical theory poses restrictions on what can be considered
as observable and what is not; such restrictions can be seen as the effect of
some kind of superselection rule. Finally, we develop a concrete example and we
discuss possible effects on the heterodyne spectrum of a two-level system due
to a structured thermal-like bath with memory.Comment: 23 page
On some Gaussian Bernstein processes in RN and the periodic Ornstein-Uhlenbeck process
In this article we prove new results regarding the existence of Bernstein
processes associated with the Cauchy problem of certain forward-backward
systems of decoupled linear deterministic parabolic equations defined in
Euclidean space of arbitrary dimension N, whose initial and final conditions
are positive measures. We concentrate primarily on the case where the elliptic
part of the parabolic operator is related to the Hamiltonian of an isotropic
system of quantum harmonic oscillators. In this situation there are many
Gaussian processes of interest whose existence follows from our analysis,
including N-dimensional stationary and non-stationary Ornstein-Uhlenbeck
processes, as well as a Bernstein bridge which may be interpreted as a
Markovian loop in a particular case. We also introduce a new class of
stationary non-Markovian processes which we eventually relate to the
N-dimensional periodic Ornstein-Uhlenbeck process, and which is generated by a
one-parameter family of non-Markovian probability measures. In this case our
construction requires an infinite hierarchy of pairs of forward-backward heat
equations associated with the pure point spectrum of the elliptic part, rather
than just one pair in the Markovian case. We finally stress the potential
relevance of these new processes to statistical mechanics, the random evolution
of loops and general pattern theory.Comment: Research articl
- …