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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Laplace transform of the first passage time density of theOrnstein--Uhlenbeck process for a constant threshold contains a ratio of twoparabolic cylinder functions for which no analytical inversion formula isavailable. Recently derived inverse Laplace transforms for the product of twoparabolic cylinder functions together with the convolution theorem of theLaplace transform then allow to derive a new Volterra integral equation forthis first passage time density. The kernel of this integral equation containsa parabolic cylinder function and the Fortet renewal equation for theOrnstein-Uhlenbeck process emerges as a special case, namely when the order qof the parabolic cylinder function is set at 0. The integral equation is shownto hold both for constant as well as time dependent thresholds. Moreover, thekernel of the integral equation is regular for q<=-1.

A new integral equation for the first passage time density of the Ornstein-Uhlenbeck process