A double forecasting model based on conditional expectation is proposed through probability distribution of port cargo throughput. A compound variable, being composed of the number of cargo ships arriving at the port and the operating efficiency of handling equipment, is constructed. The port cargo throughput is the sum of all compound variables which indicated the cargo throughput each time wh...

Given a probability space (Ω,F , P ), a F -measurable random variable X , and a sub-σ-algebra G ⊂ F , it is well known that the conditional expectation E[X|G] is the optimal L-predictor (also known as “the least mean square error” predictor) of X among all the G-measurable random variables [8, 11]. In this paper, we provide necessary and sufficient conditions under which the conditional expecta...

In 1953 A. Grothendieck introduced the property known as Dunford-Pettis property [18]. A Banach space X has the Dunford-Pettis property (DPP in the sequel) if whenever (xn) and (ρn) are weakly null sequences in X and X∗, respectively, we have ρn(xn) → 0. It is due to Grothendieck that every C(K )-space satisfies the DPP. Historically, were Dunford and Pettis who first proved that L1(μ) satisfie...

A type of oscillation modeled on BMO is introduced to characterize norm compactness in L 1. This result is used to characterize the bounded linear operators from L 1 into a Banach space X that map weakly convergent sequences onto norm convergent sequences (i.e. are Dunford-Pettis). This characterization is used to study the geometry of Banach spaces X with the property that all bounded linear o...

A geometric approach, analogous to the approach used in the additive case, is proposed to determine the conditional expectation with non-additive probabilities. The conditional expectation is then applied for (i) updating the probability when new information becomes available; and (ii) defining the notion of independence of non-additive probabilities and Nash equilibrium. Journal of Economic Li...

2 Review of probability. 5 2.1 Properties of expectation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Convergence of random variables. . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Convergence in probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Informati...

The paper studies the core-Walras equivalence problem in the commodity space framework of Banach spaces, allocations being defined as Pettis integrable functions. In particular, a core-Walras equivalence result for a certain class of commodity spaces is established, without requiring that the commodity space be separable. The class covered by this result includes the Lp(μ) spaces, 1 ≤ p < ∞, μ ...

Pettis raised the question whether or not separability of the range space implies almost everywhere weak differentiability of Pettis integrals. Phillips has given an example which answers this question in the negative. His construction is based on a sequence of orthogonal vectors in Hilbert space. We present here a different example of the same type of function. Our basic construction is that o...

It is shown that if (Xn)n is a Bochner integrable stochastic process taking values in a Banach lattice E, the convergence of f(Xn) to f(X) where f is in a total subset of E∗ implies the a.s. convergence. For any Banach space E-valued stochastic process of Pettis integrable strongly measurable functions (Xn)n, the convergence of f(Xn) to f(X) for each f in a total subset of E∗ implies the conver...

Abstract Recently a regular (unconditional) decision process has been mathematically formulated from the multistage decision process in Bellman and Zadeh's paper "Decision-making in a fuzzy environment". According to the available information on total fuzziness, we propose two types of conditional decision process for regular decision process. One is an "a posteriori conditional decision proces...