| 1. | A strong limit theorem for fair game and the approach of conditional moment generating function
关于公平赌博的一个强极限定理与条件矩母函数方法 |
| 2. | Secondly we study the properties of moment generating functions of probability measures , calculate its sub - differential by the convex analysis , use it to characterize the quasi - symmetric probability
本文研究了概率测度的矩母函数的性质，用凸分析的方法算出了矩母函数的次微分，并用此完全刻画了c . j . stone提出的拟对称概率测度的性质。 |
| 3. | Later , professor liu wen studied the sequences of discrete random variables by combining the analytic technique with the approach of generating function and moment generating function and obtained a class of deviation theorems [ 10 ] ~ [ 121
后来，刘文教授把分析方法结合母函数和矩母函数的方法研究了离散型随机变量，得到了一类强偏差定理。 |
| 4. | By using conditional moment generating functions and differentiation of measures on a net , some limit theorems and a class of deviation theorems of multivariate function sequences of arbitrary random variables ralated to the conditional expectations are obtained
本论文利用条件矩母函数和网微分法，得到任意随机变量多元函数序列相对于条件期望的偏差定理和极限定理。 |
| 5. | A strong deviation theorem of multivariate function sequences of arbitrary random variables is obtained by using moment generating functions and differentiation of measures on a net . and a strong deviation theorem of discrete information sources is obtained
本论文利用母函数和网微分法得到任意随机变量多元函数序列的强偏差定理；及一个对离散信源普遍成立的强偏差定理。 |
| 6. | The research methods are : using the conditional probability theory to work out the moment generating function of process s ( t ) and its distribution function ; using the increasing and declining character and the convexity to compare the lundberg exponent and the ruin probability of different processes
研究方法为:利用条件概率证明过程s ( t )的矩母函数以及其分布函数;利用增减性以及凹凸性比较lundberg指数,从而比较其相关性对破产概率的影响。 |
| 7. | Professor liu wen , who first invented analysis method in solving large number theorem , connected it with moment generating functions , conditional moment generating functions and differentiation of measures on a net , and some strong limit theorems are obtained . this paper continue to study and expand these results
刘文教授在解决大数定律中把首创的分析方法和矩母函数、条件矩母函数以及测度的网微分法结合起来，得出一系列极限结果，本论文继续并拓广这方面的研究。 |
| 8. | Fourthly we use the infimum of the moment generating function to study the a - transient and a - recurrent for random walks and levy processes , give a dichotomy theorem for not one - sided processes and prove tha t the process x is quasi - symmetric if and only if x is not a - recurrent for all a < 0 which is the probability explanation of quasi - symmetry
对于随机游动和l vy过程，我们用矩母函数的最小值讨论了他们的-常返性和-暂留性，给出非单边过程的一个二分定理，并证明了拟对称过程等价于过程对任意0都是-常返的，这是拟对称的概率意义。 |
