We derive necessary and sufficient conditions for global-in-time existence of solutions of ordinary differential, stochastic differential, and parabolic equations. The conditions are formulated in terms of complete Riemannian metrics on extended phase spaces (conditions with two-sided estimates) or in terms of derivatives of proper functions on extended phase spaces (conditions with one-sided e...

We study in this paper a class of preference relations on two distinct vector spaces representing two production choice spaces by introducing a comparison theorem for stochastic differential equations driven by a semimartingale. Some sufficient conditions on production choices which are budget-constrained by commodity prices are proposed. Key–Words:stochastic differential equations, comparison ...