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Let $V: \mathbb R^n \to \mathbb R^n$ be a Lipschitz vector field. Consider a one dimensional Brownian motion $W$ and the SDE $$dX_t = V(X_t) \, dW_t,$$ where we identify $V(X_t) \in \mathbb R^n$ with ...

We suppose $X$ solves our SDE $dX_{t}=-X_{t}dt+dW_{t}$ for $t\geq0$ with initial condition $X_{0}=0$ w.r.t to our measure $P$ on $(\Omega,\mathcal{F})$. $W_{t}$ is standard Wiener. This solution is ...