probability set
1.The new theory can be easily understood on basis of classical theories: the probability theory, the set theory, and the Shannon information theory.
2.Two methods of parameter estimation of discrete observation in HMM are proposed in this paper. One estimates the transition probability and the distribution of discrete symbol set at first. Each state is assumed to be from a Gaussian distribution.
3.In the model,generator set state is described as state probability vector,and is associated with two abutting state probability by one-step transfer probability. The effect of generator load on transfer probability is considered by step factor.
4.Through a probability problem, a connection is showed between binomial distribution and negative binomial distribution and therefore a composed formula is set up, which is proved by way of probability and algebra.
5.a commonsense rule (or set of rules) intended to increase the probability of solving some problem.
6.By introducing the transition probability parameter, we show that the general dynamic equation for which short interest rate satisfies and set up the discrete term structure model, which extends BDT model.
7.We prove that {Xn,n≥1} is an L1S-game iff it converges in probability under the condition liminf E‖XSn‖<∞ or ∫{τ<∞}‖Xτ‖dP<∞,?τ∈? where is ? the set of all stopping times with respect to {Fn,n≥1} and Sn=inf{s∈S:n≤s},n∈N.
8.A new method of absolute calibration of photodetector sensitivity based on spontaneous parametric down-conversion(SPDC) biphoton field is described.The process of SPDC is studied theoretically.The single photon detection probability and two-photon coincidence probability are derived and the calibration principle for photodetectors is explained.An experimental system has been set up.The sensitivity of a photon-counting photomultiplier tube was measured,and the results were compared with those obtained using conventional method.
9.a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success.
10.The risk assessment method on corroded oil pipeline failure with analytic solution is introduced in detail. On the basis of ASME B31G and DNV, a calculation model on failure probability of corroded pipeline is established. Combining the statistical data of pipeline accidents abroad, the consequence assessment model is set up by applying Bernoulli equation.
