English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper a new version of the chain rule for calculating the mean squarederivative of a second-order stochastic process is proven. This randomoperational calculus rule is applied to construct a rigorous mean squaresolution of the random Chebyshev differential equation (r.C.d.e.) assuming mildmoment hypotheses on the random variables that appear as coefficients andinitial conditions of the corresponding initial value problem. Such solution isrepresented through a mean square random power series. Moreover, reliableapproximations for the mean and standard deviation functions to the solutionstochastic process of the r.C.d.e. are given. Several examples, that illustratethe theoretical results, are included.

A mean square chain rule and its applications in solving the random Chebyschev differential equation