School of Mathematics and System Science Shandong University Jinan 250100 China;
Backward stochastic differential equations; Nonlinear expectation; Nonlinear expected utilities; Measure of risk; g-expectation; Nonlinear Markov chain; g-martingale; Nonlinear martingale; Nonlinear Kolmogorov's consistent theorem; Doob-Meyer decompositio;