We prove a law of the iterated logarithm for stable processes in a random scenery. The proof relies on the analysis of a new class of stochastic processes which exhibit long-range dependence.

When studying stochastic processes, it is often fruitful to understand several different notions of regularity. One such notion is the optimal Hölder exponent obtainable under reparametrization. In this paper, we show that chordal SLEκ in the unit disk for κ ≤ 4 can be reparametrized to be Hölder continuous of any order up to 1/(1 + κ/8). From this, we obtain that the Young integral is well def...

We prove that partial sums of linear multiparameter stochastic processes can be represented as partial sums of independent innovations plus components that are uniformly of smaller order. This representation is exploited to establish functional central limit theorems and strong approximations for random fields.

The paper considers a particular family of set–valued continuous time stochastic processes modeling birth–and–growth processes. The proposed setting allows us to infer the nucleation and the growth processes. A decomposition theorem is established to characterize the nucleation and the growth. As a logical consequence, different consistent set–valued estimators are studied for growth process. M...

multistage stochastic programming is a key technology for making decisions over time in an uncertain environment. one of the promising areas in which this technology is implementable, is medium term planning of electricity production and trading where decision makers are typically faced with uncertain parameters (such as future demands and market prices) that can be described by stochastic proc...

in this paper, the capacitated location-routing problem with fuzzy demands (clrp-fd) is considered. the clrp-fd is composed of two well-known problems: facility location problem and vehicle routing problem. the problem has many real-life applications of which some have been addressed in the literature such as management of hazardous wastes and food and drink distribution. in clrp-fd, a set of c...

Abstract— Studies on the effectiveness of fuzzy logic for nonlinear modeling are presented. Although successful applications of fuzzy logic in many diverse areas are reported in the literature, commonly the explicit description of the key features of fuzzy logic yielding these outcomes is not addressed. The present research addresses this issue, to understand the basic features of fuzzy logic i...

Let ( ) [ ] { } t G G t T = ∈ ω , 0, be a fuzzy stochastic process and ( ) [ ] { } t A t T ∈ ω , 0, be a real valued finite variation process. We define the Lebesgue-Stieltjes integral denoted by ( ) ( ) ∫ t s s G A ω ω 0 d for each t > 0 by using the selection method, which is direct, nature and different from the indirect definition appearing in some references. We shall show that this kind o...

This paper proposes a fuzzy-robust stochastic multiobjective programming (FRSMOP) approach, which integrates fuzzy-robust linear programming and stochastic linear programming into a general multiobjective programming framework. A chosen number of noninferior solutions can be generated for reflecting the decision-makers’ preferences and subjectivity. The FRSMOP method can effectively deal with t...

In the article an application of the fuzzy testing of hypothesis to the stochastic-signal detection problem is considered when the signal-to-noise ratio approaches zero. We first obtain the general reManuscript received March 13, 1992; revised February 1 1 , 1993. This work was supported by the Science and Engineering Foundation of Korea (KOSEF) under Grant 92 1-0800-002-2. The authors are with...