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We consider the occurrence of record-breaking events in random walks withasymmetric jump distributions. The statistics of records in symmetric randomwalks was previously analyzed by Majumdar and Ziff and is well understood.Unlike the case of symmetric jump distributions, in the asymmetric case thestatistics of records depends on the choice of the jump distribution. Wecompute the record rate $P_n(c)$, defined as the probability for the $n$thvalue to be larger than all previous values, for a Gaussian jump distributionwith standard deviation $\sigma$ that is shifted by a constant drift $c$. Forsmall drift, in the sense of $c/\sigma \ll n^{-1/2}$, the correction to$P_n(c)$ grows proportional to arctan$(\sqrt{n})$ and saturates at the value$\frac{c}{\sqrt{2} \sigma}$. For large $n$ the record rate approaches aconstant, which is approximately given by$1-(\sigma/\sqrt{2\pi}c)\textrm{exp}(-c^2/2\sigma^2)$ for $c/\sigma \gg 1$.These asymptotic results carry over to other continuous jump distributions withfinite variance. As an application, we compare our analytical results to therecord statistics of 366 daily stock prices from the Standard & Poors 500index. The biased random walk accounts quantitatively for the increase in thenumber of upper records due to the overall trend in the stock prices, and afterdetrending the number of upper records is in good agreement with the symmetricrandom walk. However the number of lower records in the detrended data issignificantly reduced by a mechanism that remains to be identified.

Record statistics for biased random walks, with an application to financial data