Stochastic Differential Equations with Markovian SwitchingThis textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry. |
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Stochastic Differential Equations With Markovian Switching Mao Xuerong,Yuan Chenggui Limited preview - 2006 |
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Amax approximate solution Assume Assumption 4.10 Assumption 6.3 asymptotically stable Chapter cidi compute continuous convergence Corollary dB(s definition denote Doob martingale equation 5.1 exists finite function Gronwall inequality Hence Hölder inequality holds independent inf{t initial data initial value Itô formula Lemma Let Assumption Let B(t lim sup linear growth condition Lipschitz condition Lyapunov exponent Markov chain Markov property matrix mean square Moreover n-dimensional non-negative nonsingular M-matrix numerical method obtain positive constant probability space R-valued random variable required assertion right-continuous Rnxm satisfying scalar Brownian motion SDDE SDE with Markovian solution of equation solution x(t stable in mean stochastic differential equation stochastic integral stochastic process sufficiently small surely exponentially stable tk+1 trivial solution unique solution V(xo αι απ