Bessel-like processes and SDE
This paper deals with the Bessel-like prosess \(X_t\), which is the square root of \(Y_t\) described by the stochastic differential equation \(dY_t=2 \sqrt Y_tdB_t+b(Y_t)dt\), \(Y_t\geq 0\), where \(B_t\) is a Brownian motion and \(b\) is a continuous function with \(b(0)>0\). Though Itô's formula yields formally the stochastic differential equation \[ X_t=X_0+B_t+\int^t_0\frac{b(X^2_s)-1}{X_s} ds,\tag{*} \] this does not hold globally in time generally. Studying the behaviour of \(Y_t\) near the boundary point 0, the author presents a condition on \(b\), so that the stochastic differential equation (*) holds. Moreover, she obtains a new stochastic equation involving the local times, which holds for general \(b\).
scientific article; zbMATH DE number 5010145