Results 211 to 220 of about 132,951 (266)
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On Stochastic Integration and Differentiation
Acta Applicandae Mathematica, 1999This short note presents a method to identify the integrands \((\varphi_j)_{j=1}^n\) for a martingale \(\xi_t=\sum_{j=1}^n\int_0^t\varphi_j d\eta^j_t\), \((\eta^j)_{j=1}^n\) being independent Brownian motions, in a measurable way. The quintessence of the method is an \(L^2\)-limit of certain approximations to the quadratic covariation between \(\xi ...
Di Nunno, G., Rozanov, Yu. A.
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Numerical differentiation by integration
Mathematics of Computation, 2013While there are various methods which have been developed for numerical differentiation, the estimation of the derivative of a function is often problematic when one has only noisy values of the function itself. In this instance it is important to employ a method which is able to calculate \(f'(x)\) in a stable manner. This article specifically focuses
Xiaowei Huang 0003 +2 more
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On the integration of differential fractions
Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, 2013In this paper, we provide a differential algebra algorithm for integrating fractions of differential polynomials. It is not restricted to differential fractions that are the derivatives of other differential fractions. The algorithm leads to new techniques for representing differential fractions, which may help converting differential equations to ...
François Boulier +3 more
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Differentiation and Integration
The Psychoanalytic Study of the Child, 1996The purpose of this paper is to propose a clinical approach to coordinating the psychoanalytic process with the developmental process in treating children. The paper is constructed as a dialogue between the spirit of Anna Freud and myself; a vignette brings together the principal traditional features Ms.
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integration and differentiation
1994The evaluation of integrals in elementary calculus is accomplished by the Fundamental Theorem of Calculus, which can be stated as follows: Let \(F(t)\) be a function for which the derivative \(F^{\prime}(t)\) exists and is a continuous function for t in the interval \(\{a \leq t \leq b\}.\)
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Differentiation und Integration
1988Das Tangentenproblem bildet aus historischer Sicht einen Ausgangspunkt der Differentialrechnung. Wir sind darauf bereits im Abschnitt 4.3.3 eingegangen und haben den Differentialquotienten geometrisch als Tangentenanstieg deuten konnen. Um fur eine Funktion f den Anstieg der Tangente in einem Punkt P = (x0, f (x0)) des Funktionsgraphen zu erhalten ...
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Differentiation and Integration
2021Let \(f\in AA(\mathbb X)\) and suppose that its derivative f′ exists and is uniformly continuous on \(\mathbb R\). Then \(f'\in AA(\mathbb X)\).
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Stochastic Integrals and Differential Measures
Theory of Probability & Its Applications, 1988The description of the class of measures with square integrable logarithmic derivative along a vector field and an operator field is obtained. This derivative coincides with an extended stochastic integral in the Gaussian case. The proofs are based on integration by parts.
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Differentiation and Integration of Differential Forms
2004Abstract Theorem 12.1 There exists one and only one operator, d, on the algebra ofdifferential forms with the following properties.
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Differentiation and Integration
2009In this chapter, we examine the mathematical foundations of differentiation and integration. The theorems of this chapter are useful not only to make calculus work but also for studying functions in many other contexts.We do not spend any time on the important applications that typically appear in courses devoted to calculus, such as optimization ...
Kenneth R. Davidson, Allan P. Donsig
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