TMS165/MSA350 Stochastic Calculus, part I. Lectures 12–13. Numerical Methods for Stochastic ODEs
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چکیده
Remark 1. The Lipschitz condition (4) is called global because it holds for all x, y ∈ R with the same constant L. Klebaner Theorem 5.4 assumes only a local Lipschitz condition, where the Lipschitz constant may depend on the size of x, y. We use a global condition in order to make the presentation simpler. Later on we will also assume a Lipschitz condition with respect to t, see (21). (There is a mistake in Theorem 5.4: the constants in (5.37) and (5.38) cannot be the same because the first one depends on N , K = KN , while the second one is a global constant, independent of N .)
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TMS165/MSA350 Stochastic Calculus, part I. Lectures 13–14. Numerical Methods for Stochastic ODEs
Remark 1. The Lipschitz condition (4) is called global because it holds for all x, y ∈ R with the same constant L. Klebaner Theorem 5.4 assumes only a local Lipschitz condition, where the Lipschitz constant may depend on the size of x, y. We use a global condition in order to make the presentation simpler. Later on we will also assume a Lipschitz condition with respect to t, see (21). (There is...
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