Study On Weak LDP Of Associated Random Variables Under Sublinear Expectation

From 20s century, Theory of large deviation has developed gradually. It has been an important branch of probability theory; The main purpose is to depict the limit of probability of type of exponent. LDP is much more precise than Law of Large Numbers, thus we could regard the LDP as the precision of Law of Large Numbers. Researching theory of LDP has great realistic meaning on financial field like insurance, etc. With the research of LDP getting more deeply, the application of LDP would become more and more wide. LDP theory become one of the most popular branch of theory of probability.Kolmogorov, one of the founders of classical theory of probability, and The former Soviet Union famous mathematician, established the axiom system of classical theory of probability. Driven by financial risk, Professor Shige Peng of Shandong University put forward a new axiom system, the theory of Sublinear Expectation, on the basis of Kolmogorov’s. Many important and significant result or theorem in classical space of probability could be proved or applied well in case of sublinear expectation. Thus, many studies field in classic space should be taken into account.Considering that many good result and theorem of LDP in case of classic space colud be proved in case of sublinear expectation. Thus in this paper we prove partial sums of strong mixing r.v. sequence satisfies the weak LDP in case of nonlinear expectation by the method of constructing rate function and the property of △ sub-additive function; besides, for existent result, i.e. "partial sums of independent r.v. sequence satisfies the weak LDP" studied by Wuhan University Professor Fuqing Gao and Dr. Mingzhou Xu, in this paper we prove it by a different method which is similar with the method of proving partial sums of strong mixing r.v. sequence satisfies the weak LDP. Besides, in this paper, we prove two corollaries which hold in the classic probability space are also correct under sublinear expectation space.In theory of LDP, there is a lot of useful tools and applications could be proved in case of sublinear expectation, believe near future there would be more and more significant result of LDP in case of sublinear expectation appear over the horizon.