| Limits of the Wong-Zakai Type with a Modified Drift Term (1989) | |||||||||||||
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| . We study Stratonovich stochastic differential equations driven by an m-dimensional Wiener process W , with m 2. If W is approximated by processes W with more regular sample paths, then it is known that the solutions of the equations driven by the W will converge to the solution of the equation driven by W , provided that the approximations satisfy the conditions of the Wong-Zakai theorem. McShane gave an example showing that, if those conditions are not satisfied, then a different limiting equation can arise. Here we describe a large class of equations, obtained from the original one by suitably modifying the drift term, that can arise as limiting equations by some choice of the sequence fW g. 1. Introduction. Consider a stochastic differential equation dx = f 0 (x)dt + m X i=1 f i (x)dW i ; (1.1) where x is n-dimensional, W = (W 1 ; : : : ; Wm ) is a standard m-dimensional Brownian motion, the vector fields f i satisfy appropriate smoothness and growth conditions, an... | |||||||||||||
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