Journal article
Continuity in a pathwise sense with respect to the coefficients of solutions of stochastic differential equations
For stochastic differential equations (SDEs) of the form dX(t) = b(X)(t)) dt + sigma(X(t))dW(t) where b and sigma are Lipschitz continuous, it is shown that if we consider a fixed sigma is an element of C-5, bounded and with bounded derivatives, the random field of solutions is pathwise locally Lipschitz continuous with respect to b when the space of drift coefficients is the set of Lipschitz continuous functions of sublinear growth endowed with the sup-norm.
Furthermore, it is shown that this result does not hold if we interchange the role of b and c. However for SDEs where the coefficient vector fields commute suitably we show continuity with respect to the sup-norm on the coefficients and a number of their derivatives.
Language: | English |
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Year: | 1997 |
Pages: | 155-179 |
ISSN: | 1879209x and 03044149 |
Types: | Journal article |
DOI: | 10.1016/S0304-4149(97)00024-0 |