A class of higher-order stochastic differential equations (Q2836972)

A procedure is developed for obtaining closed form solutions of \(n\)th-order linear stochastic differential equations of the form NEWLINE\[NEWLINEdy^{(n-1)}+ \sum^{n-1}_{i=0} \alpha_i y^{(i)}\,dt+ \sum^{n-1}_{j=0} \sigma_j y^{(f)} dw= 0,NEWLINE\]NEWLINE where \(n\geq 2\), \(\alpha_i\), \(\sigma_j\) are constants, and \(w\) is a normalized Wiener process. Several examples are provided that illustrate cases that can arise when using the procedure.