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951.
Hassan Allouba 《随机分析与应用》2013,31(2):367-380
Abstract A peculiar feature of Itô's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative of semimartingales with respect to Brownian motion that leads to a differentiation theory counterpart to Itô's integral calculus? From Itô's definition of his integral, such a derivative must be based on the quadratic variation process. We give such a derivative in this note and we show that it leads to a fundamental theorem of stochastic calculus, a generalized stochastic chain rule that includes the case of convex functions acting on continuous semimartingales, and the stochastic mean value and Rolle's theorems. In addition, it interacts with basic algebraic operations on semimartingales similarly to the way the deterministic derivative does on deterministic functions, making it natural for computations. Such a differentiation theory leads to many interesting applications, some of which we address in an upcoming article. 相似文献
952.
Abstract A Wick-Itô formula for Gaussian processes is obtained. This is a change of variables formula, which is to Wick-Itô integrals what the usual Itô formula is to Itô integrals. The conditions are weak enough to allow processes with infinite quadratic variation. They are satisfied by fractional Brownian motion with parameter 1/4 < H < 1. 相似文献
953.
G. O. S. Ekhaguere 《随机分析与应用》2013,31(5):961-993
Abstract A general approach is introduced to studying the properties of solutions of an arbitrary noncommutative stochastic differential equation (NSDE) in several interesting locally convex operator topologies, grouped into two main sets comprising the strong/λ?-topologies and the weak topologies. Results concerning the existence and uniqueness of solutions in these topologies are established. The approach is based on two reformulations of the NSDE, corresponding to the two sets of topologies, and is well-suited for characterizing, both analytically and numerically, various topological features of the solutions of an NSDE. 相似文献
954.
955.
The wavelet transform is defined for Wiener functionals. We characterize global and local regularities of Wiener functionals and we give a criterion for the existence and regularity of densities. Such a criterion is applied to diffusion processes and to the solutions to backward stochastic differential equations. 相似文献
956.
Gaspard Bangerezako 《Journal of Difference Equations and Applications》2013,19(9):1229-1249
We propose q-difference versions of some basic results of complete controllability and observability of linear systems such as criterions of controllability and observability, controllability and observability canonical forms, the q-duality theorem, the interconnection between these concepts and that of polynomials without common zeros. As an appendix, is given a simple but computationally meaningful Maple Procedure for the controllability criterion for time constant systems. 相似文献
957.
Christopher S. Goodrich 《Journal of Difference Equations and Applications》2013,19(11):1758-1780
958.
Jinfa Cai 《International Journal of Mathematical Education in Science & Technology》2013,44(6):839-855
Analysing the responses of 311 sixth-grade Chinese students and 232 sixth-grade US students to two problems involving arithmetic average, this study explored students' understanding and representation of the averaging algorithm from a cross-national perspective. Results of the study show that Chinese students were more successful than US students in obtaining correct numerical answers to each of the problems, but US and Chinese students had similar cognitive difficulties in solving the second task. The difficulties were not due to their lack of procedural knowledge of the averaging algorithm, rather due to their lack of conceptual understanding of the algorithm. There were significant differences between the US and Chinese students in their solution representations of the two average problems. Chinese students were more likely to use algebraic representations than US students; while US students were more likely to use pictorial or verbal representations. US and Chinese students' use of representations are related to their mathematical problem-solving performance. Students who used more advanced representations were better problem solvers. The findings of the study suggest that Chinese students' superior performance on the averaging problems is partly due to their use of advanced representations (e.g. algebraic). 相似文献
959.
Cinzia Bonotto Milena Basso 《International Journal of Mathematical Education in Science & Technology》2013,44(3):385-399
In common teaching practice the habit of connecting mathematics classroom activities with reality is still substantially delegated to wor(l)d problems. During recent decades, a growing body of empirical research has documented that the practice of word problem solving in school mathematics does not match this idea of mathematical modelling and mathematization. If we wish to construct ‘real problems arising from real experiences of the child’ following the spirit of these new suggestions, we have to make changes. On the one hand we have to replace the type of activity in which we delegate the process of creating an interplay between reality and mathematics by substituting the word problems with an activity of realistic mathematical modelling, i.e. of both real-world based and quantitatively constrained sense-making; and, on the other hand, to ask for a change in teacher beliefs; furthermore, a directed effort to change the classroom socio-math norms will be needed. This paper discusses some classroom activities that takes these factors into account. 相似文献
960.
Keith Jones 《International Journal of Mathematical Education in Science & Technology》2013,44(1):53-60
While proofs are central to university level mathematics courses, research indicates that some students may complete their degrees with an incomplete picture of what constitutes a proof and how proofs are developed. The paper sets out to review what is known of the student experience of mathematical proof at university level. In particular, some evidence is presented of the conceptions of mathematical proof that recent mathematics graduates bring to their postgraduate course to teach high school mathematics. Such evidence suggests that while the least well-qualified graduates may have the poorest grasp of mathematical proof, the most highly qualified may not necessarily have the richest form of subject matter knowledge needed for the most effective teaching. Some indication of the likely causes of this incomplete student perspective on proof are presented. 相似文献