Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument

We consider function $f$ which is depended on the parameters $0<a\in R$, $q_{0n}\in (0;1)$, $n\in N$ and convergent positive series $v_1+v_2+...+v_n+...$, defined by equality $f(x=\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=a^{\varphi(x)}$, where $\alpha_n\in \{0,1\}$, $\varphi(x=\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=\alpha_1v_1+...+\alpha_nv_n+...$, $q_{1n}=1-q_{0n}$, $\Delta^{Q_2^*}_{\alpha_1...\alpha_n...}=\alpha_1q_{1-\alpha_1,1}+\sum\limits_{n=2}^{\infty}\big(\alpha_nq_{1-\alpha_n,n}\prod\limits_{i=1}^{n-1}q_{\alpha_i,i}\big)$.In the paper we study structural, variational, integral, differential and fractal properties of the function $f$.

A new test for convergence of positive series

The paper provides a new test of convergence and divergence of positive series. In particular, it extends the known test by Margaret Martin [Bull. Amer. Math. Soc. 47 (1941), 452-457].

Consecutive Earnings Surprises: Small and Large Trader Reactions

ABSTRACT Prior research demonstrates that investors respond differently to earnings surprises that are part of a string of consecutive earnings increases or surprises than to those that are not. To shed light on who values these patterns, I compare trading responses of small and large traders to earnings surprises that occur during a series of positive or negative surprises. I find that the relative intensity of small traders' trading response (and, to a lesser extent, that of medium traders) to earnings surprises generally increases as a series progresses. Small traders respond more negatively to the second (third) negative surprise in a series than to the first (second), and more positively for the first three surprises in a positive series. Moreover, I find that announcement-period returns are related to the trading of small and medium traders. These results suggest that less sophisticated smaller traders, responding to earnings series, contribute to previously documented pricing patterns. Data Availability: All data used in this study, with the exception of data obtained from an anonymous discount brokerage firm, are publicly available from the sources indicated in the text.