Let (ξ1,η1), (ξ2,η2),… be independent identically distributed R2-valued random vectors. Assuming that ξ1 has zero mean and finite variance imposing three distinct groups of assumptions on the distribution η1 we prove functional limit theorems for logarithm convergent discounted perpetuities ∑k≥0eξ1+…+ξk−akη k+1 as a→0+. Also, a law iterated which corresponds to one aforementioned theorems. The ...

Abstract Research background Markov Decision Processes ( MDPs ) are a powerful framework for modeling many real-world problems with finite-horizons that maximize the reward given sequence of actions. Although such as investment and financial market where value decreases exponentially time, require introduction interest rates. Purpose This study investigates non-stationary finite-horizon discoun...

This paper is a sequel to Kurano et al [9], [10], in which the fuzzy perceptive models for optimal stopping or discounted Markov decision process is given. We proposed a method of computing the corresponding fuzzy perceptive values. Here, we deal with the average case for Markov decision processes with fuzzy perceptive transition matrices and characterize the optimal average expected reward, ca...