306 research outputs found
Exact solution of a stochastic protein dynamics model with delayed degradation
We study a stochastic model of protein dynamics that explicitly includes
delay in the degradation. We rigorously derive the master equation for the
processes and solve it exactly. We show that the equations for the mean values
obtained differ from others intuitively proposed and that oscillatory behavior
is not possible in this system. We discuss the calculation of correlation
functions in stochastic systems with delay, stressing the differences with
Markovian processes. The exact results allow to clarify the interplay between
stochasticity and delay
On the effect of heterogeneity in stochastic interacting-particle systems
We study stochastic particle systems made up of heterogeneous units. We
introduce a general framework suitable to analytically study this kind of
systems and apply it to two particular models of interest in economy and
epidemiology. We show that particle heterogeneity can enhance or decrease the
collective fluctuations depending on the system, and that it is possible to
infer the degree and the form of the heterogeneity distribution in the system
by measuring only global variables and their fluctuations
On the Gaussian approximation for master equations
We analyze the Gaussian approximation as a method to obtain the first and
second moments of a stochastic process described by a master equation. We
justify the use of this approximation with ideas coming from van Kampen's
expansion approach (the fact that the probability distribution is Gaussian at
first order). We analyze the scaling of the error with a large parameter of the
system and compare it with van Kampen's method. Our theoretical analysis and
the study of several examples shows that the Gaussian approximation turns out
to be more accurate. This could be specially important for problems involving
stochastic processes in systems with a small number of particles
Translation-invariant generalized topologies induced by probabilistic norms
In this paper we consider probabilistic normed spaces as defined by Alsina,
Sklar, and Schweizer, but equipped with non necessarily continuous triangle
functions. Such spaces endow a generalized topology that is
Fr\'echet-separable, translation-invariant and countably generated by radial
and circled 0-neighborhoods. Conversely, we show that such generalized
topologies are probabilistically normable.Comment: 8 pages. Some minor changes and corrections have been mad
Quotient probabilistic normed spaces and completeness results
We introduce the concept of quotient in PN spaces and give some examples. We
prove some theorems with regard to the completeness of a quotient.Comment: 10 page
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