This book provides recent results on the stochastic approximation
of systems by weak convergence techniques. General and particular
schemes of proofs for average, diffusion, and Poisson
approximations of stochastic systems are presented, allowing one to
simplify complex systems and obtain numerically tractable models.
The systems discussed in the book include stochastic additive
functionals, dynamical systems, stochastic integral functionals,
increment processes and impulsive processes. All these systems are
switched by Markov and semi-Markov processes whose phase space is
considered in asymptotic split and merging schemes. Most of the
results from semi-Markov processes are new and presented for the
first time in this book.
General
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