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abstract:
In recent work with Arnulf Jentzen and Martin Hutzenthaler we consider regularity of the solution to a stochastic differential equation (SDE) with respect to the initial value. In my talk I will explain why this type of regularity is relevant for proving convergence rates of numerical schemes to SDEs and for proving so-called `strong completeness' of the SDE.
A general theory for regularity with respect to the initial value is available for SDEs which satisfy the so-called `monotonicity condition', but little is known if this condition fails to hold. In my talk I will explain the approach we developed to deal with equations that do not satisfy the monotonicity condition, and provide examples of SDEs to which our approach can be applied. |
