We consider the one-dimensional stochastic equation [formula] for a continuous local martingale M with square variation [M] and measurable drift and diffusion coefficients b and σ. The main purpose of this paper is to derive a necessary condition for the existence of a solution X starting from x0. As a result, we construct a diffusion coefficient σ such that the above stochastic equation has no solution X whatever the initial value x0 and the non-zero, say, continuous drift coefficient b might be.
The aim of this paper is to examine whether there is any possibility to compare thevalue of someone’s existence with his nonexistence. The final conclusion is thatsuch a comparative evaluation can never be made in a meaningful and valid manner. Nobody can know as well whether he would be better off or worse off created thanhe would have been had he never existed.
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