Limit theorems for discounted convergent perpetuities

Functional limit theorems for divergent perpetuities in the contractive case*

Let ( Mk, Qk ) k∈N be independent copies of an R -valued random vector. It is known that if Yn := Q1+M1Q2+ . . .+M1 · . . . ·Mn−1Qn converges a.s. to a random variable Y , then the law of Y satisfies the stochastic fixed-point equation Y d = Q1 +M1Y , where (Q1,M1) is independent of Y . In the present paper we consider the situation when |Yn| diverges to∞ in probability because |Q1| takes large...

Limit theorems for mergesort

Central and local limit theorems (including large deviations) are established for the number of comparisons used by the standard top-down recursive mergesort under the uniform permutation model. The method of proof utilizes Dirichlet series, Mellin transforms and standard analytic methods in probability theory.

Existence of the Limit Value of Two Person Zero-Sum Discounted Repeated Games via Comparison Theorems

We give new proofs of existence of the limit of the discounted values for two person zero-sum games in the following frameworks: incomplete information, absorbing, recursive. The idea of these new proofs is to use some comparison criteria. AMS Classification: 91A15, 91A20, 49J40, 47J20

Limit Theorems for Bivariate Appell

Consider the stationary linear process X t = P 1 u=?1 a(t?u) u , t 2 Z, where f u g is an i.i.d. nite variance sequence. The spectral density of fX t g may diverge at the origin (long-range dependence) or at any other frequency. Consider now the quadratic form Q N = P N t;s=1 b(t ? s)P m;n (X t ; X s), where P n;m (X t ; X s) denotes a non-linear function (Appell polynomial). We provide general...

Local Limit Theorems for Free