Convergence of Discretized Stochastic (Interest Rate) Processes with Stochastic Drift Term

1 SUMMARY For applications in finance, we study the stochastic differential equation dX s = (2βX s +δ s)ds+g(X s)dB s with β a negative real number, g a continuous function vanishing at zero which satisfies a Hölder condition and δ a measurable and adapted stochastic process such that t 0 δ u du < ∞ a.e. for all t ∈ IR + and which may have a random correlation with the process X itself. In this paper, we concentrate on the Euler discretization scheme for such processes and we study the convergence in L 1-supnorm and in H 1-norm towards the solution of the stochastic differential equation with stochastic drift term. We also check the order of strong convergence.