# Continuity in a Pathwise sense with Respect to the Coefficients of Solutions of Stochastic Differential Equations

- Authors:
- Abstract:
- For SDE's 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 ifwe consider a fixed sigma in C^5, bounded and with boundedderivatives, the random field of solutions is pathwise locallyLipschitz continuous with respect to b when the space of driftcoefficients is the set of Lipschitz continuous functions of sublineargrowth endowed with the sup-norm. Furthermore it is shown that thisresult does not hold if we interchange the role of b and sigma.However for SDE's where the coefficient vector fields commutesuitably we show continuity with respect to the sup-norm on thecoefficients and a number of their derivatives.
- Type:
- Report
- Language:
- English
- Main Research Area:
- Science/technology
- Publication Status:
- Published
- Review type:
- Peer Review
- Submission year:
- 1996
- Publication year:
- 1996
- Scientific Level:
- Scientific
- ID:
- 2185751272