1ST-PASSAGE PROBLEMS IN LINEAR BIASED CORRELATED WALKS
The basic difference equations for biased correlated walks on an infinite line are solved by means of the Fourier-Laplace techniques. In terms of these solutions the discrete Laplace transforms of first-passage probabilities with directions are obtained. By using the latter the one-side return proba...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 1992 |
| País: | México |
| Institución: | Universidad Nacional Autónoma de México |
| Repositorio: | Sistema de Información de la Facultad de Ciencias, UNAM |
| OAI Identifier: | oai:repositorio.fciencias.unam.mx:11154/3563 |
| Acceso en línea: | http://hdl.handle.net/11154/3563 |
| Access Level: | acceso abierto |
| Palabra clave: | Engineering, Multidisciplinary Mathematics, Interdisciplinary Applications Mechanics RANDOM WALK BIASED WALK CORRELATED WALK DEGREE OF BIAS DEGREE OF CORRELATION |
| Sumario: | The basic difference equations for biased correlated walks on an infinite line are solved by means of the Fourier-Laplace techniques. In terms of these solutions the discrete Laplace transforms of first-passage probabilities with directions are obtained. By using the latter the one-side return probabilities from the positive (negative) side, R+(R-), are obtained as follows: R+ = 1/2(1 + delta) - 1/2-epsilon(1 + 3-delta + epsilon)(1 + epsilon-delta)-1, R = 1/2(1 - delta - epsilon), where delta and epsilon are the degree of correlation and the degree of anisotropy, respectively, with the ranges 0 less-than-or-equal-to delta less-than-or-equal-to 1 and 0 less-than-or-equal-to epsilon less-than-or-equal-to 1-delta. The above results are obtained with the condition that the walker initially arrived at the origin with the right step (positive direction). |
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