特殊半鞅的一个局部性质

本文讨论特殊半鞅的一个局部性质,将局部（平方可积）鞅的结果推广到了一类特殊半鞅的情形。     

Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences

We study limit distribution of partial sums S_N,k(t) = _{s = 1} ^{[N t]} A_k(X_s) of Appell polynomials of the long-range dependent moving average process X_t> = _{i t} b_{t - i i}, where {_i} is a strictly stationary and weakly dependent martingale difference sequence, and b_i i^{d - 1} (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums S_N,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { _i}.     

关于解析凸性的注记

本文研究了解析一致凸性Ｂａｎａｃｈ空间,证明了重赋范定理并且给出了具有解析一致凸性的一些具体空间。     

On Positive Random Objects

The idea of defining the expectation of a random variable as its integral with respect to a probability measure is extended to certain lattice-valued random objects and basic results of integration theory are generalized. Conditional expectation is defined and its properties are developed. Lattice valued martingales are also studied and convergence of sub- and supermartingales and the Optional Sampling Theorem are proved. A martingale proof of the Strong Law of Large Numbers is given. An extension of the lattice is also studied. Studies of some applications, such as on random compact convex sets in R ⁿ and on random positive upper semicontinuous functions, are carried out, where the generalized integral is compared with the classical definition. The results are also extended to the case where the probability measure is replaced by a -finite measure.     

Clarkson不等式与Banach空间几何

我们证明了Banach空间X是Clarkson p型（q余型）当且仅当X是一个特殊的p一致光滑空间（q-一致凸空间（）,我们还找到刻划型（余型）的一系列鞅不等式,同时,我们得到了均方函数sharp不等式。     

A law of the iterated logarithm for processes with independent increments

ＡＬＡＷＯＦＴＨＥＩＴＥＲＡＴＥＤＬＯＧＡＲＩＴＨＭＦＯＲＰＲＯＣＥＳＳＥＳＷＩＴＨＩＮＤＥＰＥＮＤＥＮＴＩＮＣＲＥＭＥＮＴＳＷＡＮＧＪＩＡＧＡＮＧ（汪嘉冈）（ＥａｓｔＣｈｉｎａＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅ＆Ｔｅｃｈｎｏｌｏｇｙ,Ｓｈａｎｇ...     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

两指标B值鞅空间的对偶

通过引入新型两指标B值鞅空间, 利用两指标B值鞅的Fefferman不等式, 证明了当B为自反Banach空间时, 由p均方算子定义的两指标B值鞅空间_pH_α     

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.