2,328 research outputs found
The Numerical Invariant Measure of Stochastic Differential Equations With Markovian Switching
The existence and uniqueness of the numerical invariant measure of the
backward Euler-Maruyama method for stochastic differential equations with
Markovian switching is yielded, and it is revealed that the numerical invariant
measure converges to the underlying invariant measure in the Wasserstein
metric. Under the polynomial growth condition of drift term the convergence
rate is estimated. The global Lipschitz condition on the drift coefficients
required by Bao et al., 2016 and Yuan et al., 2005 is released. Several
examples and numerical experiments are given to verify our theory.Comment: 25 pages, 4 figure
Invariant Measures for Path-Dependent Random Diffusions
In this paper, we investigate the existence and uniqueness of invariant measure of stochastic functional differential equations with Markovian switching. Under an average condition, we prove that there is a unique measure for the exact solutions and the corresponding Euler numerical solutions. Moreover, the invariant measure of the Euler numerical solutions will converge to that of the exact solutions as the step size tends to zero
Pinning dynamic systems of networks with Markovian switching couplings and controller-node set
In this paper, we study pinning control problem of coupled dynamical systems
with stochastically switching couplings and stochastically selected
controller-node set. Here, the coupling matrices and the controller-node sets
change with time, induced by a continuous-time Markovian chain. By constructing
Lyapunov functions, we establish tractable sufficient conditions for
exponentially stability of the coupled system. Two scenarios are considered
here. First, we prove that if each subsystem in the switching system, i.e. with
the fixed coupling, can be stabilized by the fixed pinning controller-node set,
and in addition, the Markovian switching is sufficiently slow, then the
time-varying dynamical system is stabilized. Second, in particular, for the
problem of spatial pinning control of network with mobile agents, we conclude
that if the system with the average coupling and pinning gains can be
stabilized and the switching is sufficiently fast, the time-varying system is
stabilized. Two numerical examples are provided to demonstrate the validity of
these theoretical results, including a switching dynamical system between
several stable sub-systems, and a dynamical system with mobile nodes and
spatial pinning control towards the nodes when these nodes are being in a
pre-designed region.Comment: 9 pages; 3 figure
Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control
In this paper we investigate parametrization-free solutions of the problem of
quantum pure state preparation and subspace stabilization by means of
Hamiltonian control, continuous measurement and quantum feedback, in the
presence of a Markovian environment. In particular, we show that whenever
suitable dissipative effects are induced either by the unmonitored environment
or by non Hermitian measurements, there is no need for feedback control to
accomplish the task. Constructive necessary and sufficient conditions on the
form of the open-loop controller can be provided in this case. When open-loop
control is not sufficient, filtering-based feedback control laws steering the
evolution towards a target pure state are provided, which generalize those
available in the literature
Dynamical Behavior of a stochastic SIRS epidemic model
In this paper we study the Kernack - MacKendrick model under telegraph noise.
The telegraph noise switches at random between two SIRS models. We give out
conditions for the persistence of the disease and the stability of a disease
free equilibrium. We show that the asymptotic behavior highly depends on the
value of a threshold which is calculated from the intensities of
switching between environmental states, the total size of the population as
well as the parameters of both SIRS systems. According to the value of
, the system can globally tend towards an endemic case or a disease
free case. The aim of this work is also to describe completely the omega-limit
set of all positive solutions to the model. Moreover, the attraction of the
omega-limit set and the stationary distribution of solutions will be pointed
out.Comment: 16 page
A stochastic differential equation SIS model on network under Markovian switching
We study a stochastic SIS epidemic dynamics on network, under the effect of a
Markovian regime-switching. We first prove the existence of a unique global
positive solution, and find a positive invariant set for the system. Then, we
find sufficient conditions for a.s. extinction and stochastic permanence,
showing also their relation with the stationary probability distribution of the
Markov chain that rules the switching. We provide an asymptotic lower bound for
the time average of the solution sample path, under the conditions ensuring
stochastic permanence. From this bound we are able to prove the existence of an
invariant probability measure
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