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The SDEs \begin{equation} dZ_t = \mu(t,Z_t)dt + \sigma(t,Z_t)dW_t \end{equation} with prescribed initial conditions are well studied. My question came up in my research and I have not found much on ...

I am asking an extension of the question here for SDEs of the Ito form. Consider the SDE $dX_t =\sigma(X_t) dW_t$, where $W$ is a $d$-dimensional Brownian motion and $\sigma:\mathbb{R}^n\to \mathbb{R}...

I'm looking for a result of the form: Let $B_\epsilon$ denote a "natural" smooth $\epsilon$-approximation to an $n$-dimensional Brownian motion $B$ (e.g. by mollification or simply piecewise linear) ...