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Stochastic Differential Equations and Applications
This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and
Stochastic Differential Equations With Markovian Switching
TLDR
This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching at an introductory level but emphasizes current advanced level research trends.
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
TLDR
This work gives a convergence result for Euler--Maruyama requiring only that the SDE is locally Lipschitz and that the pth moments of the exact and numerical solution are bounded for some p >2 and shows that the optimal rate of convergence can be recovered if the drift coefficient is also assumed to behave like a polynomial.
Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays
TLDR
Improved delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian delay systems are obtained by introducing some slack matrix variables and the conservatism caused by either model transformation or bounding techniques is reduced.
A Stochastic Differential Equation SIS Epidemic Model
TLDR
It is proved that this classical susceptible-infected-susceptible epidemic model is formulated as a stochastic differential equation (SDE) for the number of infectious individuals and that this SDE has a unique global positive solution.
Convergence of Monte Carlo Simulations involving the Mean-Reverting Square Root Process
The mean-reverting square root process is a stochastic differential equation (SDE) that has found considerable use as a model for volatility, interest rate, and other financial quantities. The
Exponential stability of stochastic delay interval systems with Markovian switching
  • X. Mao
  • Mathematics
    IEEE Trans. Autom. Control.
  • 10 December 2002
TLDR
The system discussed is the stochastic delay interval system with Markovian switching, which is a very advanced system and takes all the features of interval systems, Ito equations, and Markovians switching, as well as time lag, into account.
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