3,644 research outputs found
Approximate solutions for a class of doubly perturbed stochastic differential equations
In this paper, we study the Carathéodory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carathéodory approximation procedure, we prove that DPSDEs have a unique solution and show that the Carathéodory approximate solution converges to the solution of DPSDEs under the global Lipschitz condition. Moreover, we extend the above results to the case of DPSDEs with non-Lipschitz coefficients
Strong convergence of a positive preserving drift-implicit Euler scheme for the fixed delay CIR process
In this paper, we consider a fixed delay Cox-Ingersoll-Ross process (CIR
process) on the regime where it does not hit zero, the aim is to determine a
positive preserving implicit Euler Scheme. On a time grid with constant
stepsize our scheme extends the scheme proposed by Alfonsi in 2005 for the
classical CIR model. Furthermore, we consider its piecewise linear
interpolation, and, under suitable conditions, we establish the order of strong
convergence in the uniform norm, thus extending the results of Dereich et al.
in 2011.Comment: 24 page
Neutral stochastic functional differential equations with Levy jumps under the local Lipschitz condition
In this paper, a general neutral stochastic functional differential equations with infinite delay and Lévy jumps (NSFDEwLJs) is studied. We investigate the existence and uniqueness of solutions to NSFDEwLJs at the phase space Cg under the local Carathéodory type conditions. Meanwhile, we also give the exponential estimates and almost surely asymptotic estimates of solutions to NSFDEwLJs
Nonlinear Systems
Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems
Approximation of Fractional Order Conflict-Controlled Systems
We consider a conflict-controlled dynamical system described by a nonlinear
ordinary fractional differential equation with the Caputo derivative of an
order Basing on the finite-difference
Gr\"{u}nwald-Letnikov formulas, we propose an approximation of the considered
system by a system described by a functional-differential equation of a
retarded type. A mutual aiming procedure between the initial
conflict-controlled system and the approximating system is given that
guarantees the desired proximity between their motions. This procedure allows
to apply, via the approximating system, the results obtained for
functional-differential systems for solving control problems in fractional
order systems. Examples are considered, results of numerical simulations are
presented.Comment: Submitted to Progress in Fractional Differentiation and Application
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