previous theorem indicates that potential functions which approximate the expected optimization time in the respective point are good candidates likely to satisfy the additive drift condition. In the next section, we will see such a potential function suitable for the analysis of the optimization behavior of the (1+1) Evolutionary Algorithm on linear functions.

A Multiplicative Drift Theorem
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The drift theorem presented in this subsection can be considered as the multiplicative version of the classical additive result. Since we derive it from the original result, it is clear that the multiplicative version cannot be stronger than the original theorem.

\[Multiplicative Drift\] \[thm:multidrift\] Let $ S\subseteq\mathbb{R}$ be a finite set of positive numbers with minimum $s_{\min}$. Let $\{X^{(t)}\}_{t\in\mathbb{N}}$ be a sequence of random variables over $ S\cup\{0\}$. Let $T$ be the random variable that denotes the first point in time $t\in\mathbb{N}$ for which $X^{(t)}=0$.

Suppose that there exists a constant $\delta>0$ such that $$\label{eq:multidrift}
{\ensuremath{\operatorname{E}}}\big[X^{(t)}-X^{(t+1)}{\,\big|\,}X^{(t)}= s\big]\ge \delta s$$ holds for all $s\in S$ with ${\ensuremath{\mathrm{Pr}}}[X^{(t)}= s]>0$. Then for all $s_0\in S$ with ${\ensuremath{\mathrm{Pr}}}[X^{(0)}=s_0]>0$, $${\ensuremath{\operatorname{E}}}\big[T{\,\big|\,}X^{(0)}=s_0\big] \le \frac{1+\ln(s_0/s_{\min})}{\delta}.$$

Like for the notion of additive drift, we say that the drift of a random process $\{x^{(t)}\}_{t\in\mathbb{N}}$ with respect to a potential function $g$ is 