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Derivative with respect to initial condition for the solution of an SDE

Suppose we have an SDE (assuming the Lipschitz continuous conditions required for the existence of the solution): \begin{align} dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t \end{align} and define its ...
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1 answer
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Differentiable dependence on the initial condition of the solution of a SDE

Let $b,\sigma:\mathbb R\to\mathbb R$ be differentiable and Lipschitz continuous $(\Omega,\mathcal A,\operatorname P)$ be a probability space $(\mathcal F_t)_{t\ge0}$ be a complete and right-...