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

Let $(B(t))_{t\in [0,1]}$ be the linear Brownian motion and $(X_n(t))_{t\in[0,1]}$ be the $(n-1)$-fold integral of Brownian motion, $n$ being a positiveinteger:  $$ X_n(t)=\int_0^t \frac{(t-s)^{n-1}}{(n-1)!} \,\dd B(s) for any $t\in[0,1]$.$$  In this paper we construct several bridges between times 0 and 1 of theprocess $(X_n(t))_{t\in [0,1]}$ involving conditions on the successivederivatives of $X_n$ at times 0 and 1. For this family of bridges, we make acorrespondance with certain boundary value problems related to theone-dimensional polyharmonic operator. We also study the classical problem ofprediction. Our results involve various Hermite interpolation polynomials.

international journal of stochastic analysis

A class of bridges of iterated integrals of Brownian motion related to  various boundary value problems involving the one-dimensional polyharmonic  operator