The completeness research on fuzzy stochastic analysis

Covariation de convolution de martingales

We give stopped Doob inequalities for p-th moment, 0<p<∞, of stochastic convolution integrals ∫(0,t] U(t,s)φ s − dM s in a Hilbert space, where M is a Hilbert space-valued cadlag square integrable martingale, φ is an operator-valued predictable process and U(t,s) is a contraction-type evolution operator. We also generalize the previous results and try to get smaller constants. 1This research was partially supported by Sharif University of Technology.

Let $M$ be a locally square integrable martingale with predictable quadratic variance $\\langle M\\rangle$ and let $\\Delta M = M - M_-$ be the jump process of $M$. In this paper, under the various restrictions on $\\Delta M$, the different increasing rates of $M$ in terms of $\\langle M\\rangle$ are obtained. For stochastic integrals $X = B \\cdot M$ of the predictable process $B$ with respect to $M$, the a.s. asymptotic behavior of $X$ is also discussed under restrictions on the rates of increase of $B$ and the restrictions on the conditional distributions of $\\Delta M$ or on the conditional moments of $\\Delta M$. This is applied to some simple examples to determine the convergence rates of estimators in statistics.

After introducing cylindrical Gaussian random variables and Hilbert space valued Gaussian random variables, we define cylindrical Wiener process and Hilbert space valued Wiener process in a natural way. We develop the Itô stochastic integral with respect to cylindrical and Hilbert space valued Wiener processes simultaneously as they share many common features. Our construction of the Itô integral is consistent with the construction of a stochastic integral with respect to square integrable martingales, however, regarding measurability, we assume only that the integrand is adapted, following the classical ideas as presented by Liptser and Shiryayev (Statistics of Stochastic Processes. Nauka, ) and by Øksendal (Stochastic Differential Equations. Springer, New York, ). We provide detailed proofs of properties of the Itô integral and follow with the Martingale Representation Theorem. Our unified approach to stochastic integration with respect to cylindrical and Hilbert space valued Wiener processes allowed us to present the Stochastic Fubini Theorem and the Itô Formula in both cases in an almost identical way.

Uncertainties are inherently present in structural parameters such as loadings, boundary conditions or resistance of structural materials. Especially material properties and parameters of wood are strongly varying in consequence of growth and environmental conditions. To include this variation in structural analysis, available data needs to be modelled appropriately, e.g. by means of probability and, furthermore, fuzzy probability based random variables or fuzzy sets. In order to comprehend uncertainties induced by estimating the distribution parameters, the stochastic approach has been extended by fuzzy distribution parameters to fuzzy probability based random variables according to studies by Moller et al. To cope with epistemic uncertainties for e.g. geometric parameters of knotholes, fuzzy sets are used. The consequence for wooden structures is determined by fuzzy stochastic analysis in combination with a Finite Element (FE) simulation using a model suitable for characteristics of a timber structure by Jenkel and Kaliske.

Right continuous fuzzy set-valued stochastic processes with left limitation

In real situations particularly in business processes, the probability distributions are not known or imprecise and conventional modeling approaches may be questionable. Fuzzy simulation is capable of modeling uncertainties and vagueness. This paper introduces a novel approach based of fuzzy business process simulation (FBPS) and data envelopment analysis (DEA) for re-engineering, assessment and optimization of a purchasing management system. An actual purchasing system is studied and various data were collected through standard methods. The users of the purchasing management verified that the goals of a re-engineering model are to create a process-oriented approach in order to reduce purchasing process cycle time, faster customer response time and lower cost. The results of fuzzy simulation approach are compared with conventional simulation by t-test. It is shown the performance of the actual system is modeled and improved by the fuzzy simulation approach of this study. The results of fuzzy simulation are more accurate and similar to real situations than previous results by conventional simulation. In addition, DEA is used to identify optimal solution among proposed alternatives. This is the first study that introduces an integrated FBPS-DEA for optimization of purchasing management systems.

We consider cadlag local martingales M with initial value zero and jumps larger than a for some a larger than or equal to -1, and prove Novikov-type criteria for an exponential local martingale to be a uniformly integrable martingale. We obtain criteria using both the quadratic variation and the predictable quadratic variation. We prove optimality of the coefficients in the criteria. As a corollary, we obtain a verbatim extension of the classical Novikov criterion for continuous local martingales to the case of local martingales with initial value zero and nonnegative jumps.

Existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian condition

Structural analysis and design optimization have recently been extended to stochastic approach to take various uncertainties into account. However in areas whwew it is not possible to produce accurate statistical information, the probabilistic method is not appropriate for stochastic structural analysis and design optimization, since improper modeling of uncertainty could cause greater degree of statistical uncertainty than those of physical uncertainty. For uncertainty with insufficient information, possibility-based (or fuzzy set) methods have recently been introduced in stochastic structural analysis and design optimization. The main advantage of the fuzzy analysis is that it preserves the intrinsic random nature of physical variables through their membership functions and, when used for evaluation of designs, yields more conservative design than those from the probabilistic methods. There are two computational aspects in the fuzzy analysis compared to the probability analysis. First, the input fuzzy variables can be defined easier than the input random variables when no or very limited statistical data are available. Secondly, extended fuzzy operations are much simpler than those required to use probability, especially when a number of variables are involved. For possibility-based design optimization (PBDO), like for reliability-based design optimization (RBDO), the performance measure approach (PMA) with an inverse fuzzy analysis is more appropriate than other approaches, such as a possibility index approach. This paper proposes a new formulation of PBDO using PMA. It is also found that PBDO is more desirable than RBDO, since PBDO can inherently handle a system level possibility unlike RBDO. For the inverse fuzzy analysis, the maximal possibility search (MPS) method is proposed to improve numerical efficiency and accuracy comparing with the vertex method and the

Starting from fuzzy real numbers with an arbitrary lattice of belief and following the extension principle, we develop concepts of fuzzy probabilities, transition probabilities and random variables and of their combinations, and show that these concepts are consistent. We derive some results on fuzzy real numbers, on the expectation of fuzzy random variables and on fuzzy stochastic processes. To sketch the range of applications of fuzzy stochastics, we give two examples that show how real-world problems may be modeled by means of fuzzy probabilities and that give small numerical examples. Moreover, we give a brief outlook for a possible expansion of our theory to fuzzy Markovian decision processes by means of a partial order on the set of all fuzzy real numbers.

Proposes an extraction method for sea surface temperature (SST) information in the local region from NOAA AVHRR data. The method applied to the remote-sensed SST data consists of: (i) fuzzy regression analysis for NOAA AVHRR data and Landsat TM data; (ii) fuzzy level-slice processing; and (iii) feature extraction using information of neighbor pixels. Experimental results have verified the usefulness and accuracy of the proposed approach.

We analyze the risk of rural drinking water safety project and build rural drinking water safety index system, We summarize existing project risk assessment method by taking rural drinking water safety into consideration. The selection process is based on fuzzy network analysis and how rural drinking water safety project risk assessment model is constructed based on it. Empirical analysis shows that the fuzzy analytic network process evaluate rural drinking water safety project risk quantitatively, and provide theoretical basis for project control and avoiding the risks of involved parties.

Energy saving is a long strategic mission and current pressing task. The paper analyzes the situation and problem existing in the supplying and consuming of energy in Jiangsu Province. By studying the guidance idea, meanings and characteristics, it constructs the index system of comprehensive evaluation of Jiangsu Province, adopts the triangle fuzzy number method to make the rank of evaluation, combines the fuzzy mathematic and analysis hierarchy process, provides the model of comprehensive evaluation of energy saving potential. It takes the data of industry, lives and transport etc which is the main consuming energy types to above model and validates the effectiveness of the model and the method. Finally, it gives the policy and suggestion of constructing the energy saving social of Jiangsu Province from the pattern of production and consumption, management support system and technological support system.

Phosphogypsum (PG) is the waste product of phosphoric acid. Global PG production is estimated at around 160 Mt / year (AIEA, 2013). This enormous generated amount of PG produces a serious dilemma and costly management costs. This environmental issue has aroused interest in the scientific community, as evidenced by the increasing number of publications on the PG in recent years. Our work describes the Tunisian PG by-product, the storage method and the different recovery techniques studied around the world. In this work, we developed a new approach to help group decision-makers to deal with the complex PG valuation problems. This approach consists in using the Gray Rational Analysis method (GRA) to combine the decision matrices of decision makers in order to make a group decision, using the fuzzy hierarchical analysis process (Fuzzy AHP) to find the fuzzy weights criteria and contained by application the order of preference technique by similarity with fuzzy the ideal solution (Fuzzy TOPSIS) to find the best ranking of the alternatives studied. The results are accepted by the expert group, hoping for its real application.