The modified Craig–Sneyd (MCS) scheme is a promising splitting scheme of the ADI type for multi-dimensional pure diffusion equations having mixed spatial-derivative terms. In this paper we investigate the extension of the MCS scheme to two-dimensional convection–diffusion equations with a...

Let [sigma]>0,[delta]>=1,b>=0, 0<p<1. Let [lambda] be a continuous and positive function in . Using the technique of moving domains (see Russo and Trutnau (2005) [9]), and classical direct stochastic calculus, we construct for positive initial conditions a pair of continuous and positive semimartingales with and where the symmetric local times , of the respective semimartingales are related through the formula Well-known special cases are the (squared) Bessel processes (choose [sigma]=2, b=0, and [lambda]2[reverse not equivalent]0, or equivalently ), and the Cox-Ingersoll-Ross process (i.e. R, with [lambda]2[reverse not equivalent]0, or equivalently ). The case 0<[delta]<1 can also be handled, but is different. If p>1, then there is no solution.

Quantitative aspects of adjustment processes in economic growth remain frequently unsolved or are tackled with bulky or inaccurate methods like multiple shooting or log-linearization. Mulligan's (1991) method of time elimination, however, has improved the analysis of saddle path dynamics in...

We consider a neo-classical model of optimal economic growth with c.r.r.a. utility in which the traditional deterministic trends representing population growth, technological progress, depreciation and impatience are replaced by Brownian motions with drift. When transformed to 'intensive' units,...

We consider a neo-classical model of optimal economic growth with c.r.r.a. utility in which the traditional deterministic trends representing population growth, technological progress, depreciation and impatience are replaced by Brownian motions with drift. When transformed to 'intensive' units,...