We prove upper bounds for the probability that a radial SLE$_{\kappa}$ curve comes within specified radii of $n$ different points in the unit disc. Using this estimate, we then prove a similar upper bound for the probability that a whole-plane SLE$_{\kappa}$ passes near any $n$ points in the complex plane. We then use these estimates to show that the lower Minkowski content of both the radial and whole-plane SLE$_{\kappa}$ traces has finite moments of any order.For $\kappa \leq 4$, the reverse flow of the Loewner equation driven by $\sqrt{\kappa}B_t$ generates a random continuous function $\phi: \R^+ \to \R^+$ called the conformal welding. In studying backward SLE, this plays the roll of the global random object, rather than the SLE trace. Given any $x,y>0$ we use the Girsanov theorem to construct a family of probability measures, depending on some parameters, under which the conformal welding satisfies $\phi(x)=y$ almost surely. For one such law, we prove a one-point estimate for the backward SLE welding and show how it coincides with the Green's function. In another case, we decompose the law of the welding conditioned to pass through $(x,y)$ into two pieces. Using this decomposition, we integrate this law over a set $U\subset [0,\infty)\times[0,\infty)$ to get a new measure on weldings which is absolutely continuous with respect to the original backward SLE welding. Moreover, the Radon-Nikodym derivative is given by the capacity time that the graph of $\phi$ spends in $U$. In the last chapter, we study a generalization of the chordal Loewner equation called chordal measure driven Loewner evolution. We show existence of a solution to the equation, and a one-to-one correspondence between the appropriate measures and all continuously growing families of $\H$-hulls. In \cite{MS}, the notion of measure driven Loewner evolution was first introduced in the radial setting, and a similar theorem was proven. This result is pure complex analysis, without any reference to probability theory.
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