In this paper, we study properties of the stationary harmonic measure which are unique to case. We prove that any subset with an appropriate sub-linear horizontal growth has a non-zero measure. On other hand, show at least linear will have 0 every point. This result is fundamental future DLA. As application possible aggregation process rates proportional non zero all times.

In this paper, we consider a dynamic and decentralized market modeled by a noncooperative networked bargaining game. Our goal is to study how the network structure of the market and the role of middlemen influence the market’s efficiency and fairness. We introduce the concept of limit stationary equilibrium in a general trading network and use it to analyze how endogenous delay emerges in trade...

We study general state-space Markov chains that depend on a parameter, say, . Sufficient conditions are established for the stationary performance of such a Markov chain to be differentiable with respect to . Specifically, we study the case of unbounded performance functions and thereby extend the result on weak differentiability of stationary distributions of Markov chains to unbounded mapping...

Shannon’s source entropy formula is not appropriate to measure the uncertainty of non-stationary processes. In this paper, we propose a new entropy measure for non-stationary processes, which is greater than or equal to Shannon’s source entropy. The maximum entropy of the non-stationary process has been considered, and it can be used as a design guideline in cryptography.