Diffusions, Exit Time Moments and Weierstrass Theorems

Diffusions, Exit Time Moments and Weierstrass Theorems

Let Xtbe a one-dimensional diffusion with infinitesimal generator given by the operator $L = \frac{1}{2} (a(x)\frac{d}{dx})^{2} + b(x)\frac{d}{dx}$ where a(x) is a smooth, positive real-valued function and the ratio of a(x) and b(x) is a constant. Given a compact interval, we prove a Weierstrass-typ...

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Veröffentlicht in:Proceedings of the American Mathematical Society. - American Mathematical Society, 1950. - 132(2004), 8, Seite 2465-2474
1. Verfasser: de la Peña, Victor H. (VerfasserIn)
Weitere Verfasser: McDonald, Patrick
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2004
Zugriff auf das übergeordnete Werk:Proceedings of the American Mathematical Society
Schlagworte:Brownian Motion Exit Time Moments Approximation Theory Bessel Functions Physical sciences Mathematics
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520 |a Let Xtbe a one-dimensional diffusion with infinitesimal generator given by the operator $L = \frac{1}{2} (a(x)\frac{d}{dx})^{2} + b(x)\frac{d}{dx}$ where a(x) is a smooth, positive real-valued function and the ratio of a(x) and b(x) is a constant. Given a compact interval, we prove a Weierstrass-type theorem for the exit time moments of Xtand their corresponding (naturally weighted) first derivatives, and we provide an algorithm that produces uniform approximations of arbitrary continuous functions by exit time moments. We investigate analogues of these results in higher-dimensional Euclidean spaces. We give expansions for several families of special functions in terms of exit time moments. 
540 |a Copyright 2004 American Mathematical Society 
650 4 |a Brownian Motion 
650 4 |a Exit Time Moments 
650 4 |a Approximation Theory 
650 4 |a Bessel Functions 
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650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical functions  |x Continuous functions 
650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical theorems 
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650 4 |a Mathematics  |x Mathematical objects  |x Infinitesimals 
650 4 |a Mathematics  |x Mathematical objects  |x Mathematical intervals 
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650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical functions  |x Special functions 
655 4 |a research-article 
700 1 |a McDonald, Patrick  |e verfasserin  |4 aut 
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