Abstract
This chapter was born out of the need to merge two topics apparently unrelated thus far, namely:
-
(i)
the theory of relativistic interstellar flight; and
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(ii)
the stochastic processes of genetics.
Their unification is achieved by virtue of the notion of time-rescaled Brownian motion that embodies both time rescaling, typical of relativity, and Brownian motion, typical of the stochastic processes of genetics. Though the mathematics involved is not difficult, to set out the calculations in detail would require too much space. Thus, the main lines of thought only have been highlighted.
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References
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd Edition, Wiley, New York, 1971.
A. A. Borovkov, “On the First Passage Time for One Class of Processes with Independent Increments,” Theory of Probability and Applications, X(2) (1965), 331–334.
C. Maccone, “Eigenfunctions and Energy for Time-Rescaled Gaussian Processes,” Bollettino dell’Unione Matematica Italiana, Series 6, 3-A (1984), 213–220.
A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York, 1965.
W. Rindler, Special Relativity, Oliver & Boyd, Edinburgh, 1960, p. 41.
L. Arnold, Stochastic Differential Equations, Wiley, New York, 1973, pp. 84–87.
A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, 1965, p. 552.
M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press, Cambridge, 1983, pp. 36–40.
M. Kimura, “Solution of a process of random genetic drift with a continuous model,” Proc. Natl. Acad. Sci. U.S.A., 41 (1955), 144–150.
P. A. P. Moran, The Statistical Processes of Evolutionary Theory, Clarendon Press, Oxford, 1962, pp. 75–78.
M. Kimura and T. Ohta, Theoretical Aspects of Population Genetics, Princeton University Press, Princeton, NJ, 1971, pp. 167–196.
T. Maruyama, “Stochastic Problems in Population Genetics,” Lecture Notes in Biomathematics, No. 17, pp. 24–28, Springer-Verlag, Berlin, 1977.
C. Maccone, “Relativistic Interstellar Flight and Gaussian Noise,” Acta Astronautica, 17(9) (1988), 1019–1027.
C. Maccone, “Eigenfunctions and Energy for Time-Rescaled Gaussian Processes,” Bollettino dell’Unione Matematica Italiana, Series 6, 3-A (1984), 213–220.
C. Maccone, “Sur un mouvement brownien dont le temps est retardé exponentiellement,” Publications de l’Institut de Statistique de l’Université de Paris, 30 (1985), 61–72.
C. Maccone, “Special Relativity and the Karhunen—Loève Expansion of Brownian Motion,” Il Nuovo Cimento, Series B, 100 (1987), 329–342.
C. Maccone, “The Karhunen—Loève Expansion of the Zero-Mean Square Process of a Time-Rescaled Gaussian Process,” Bollettino dell’Unione Matematica Italiana, Series 7, 2-A (1988), 221–229.
C. Maccone, “Relativistic Interstellar Flight and Genetics,” Journal of the British Interplanetary Society, 43 (1990), 569–572.
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(2009). Genetics aboard relativistic spaceships. In: Deep Space Flight and Communications. Springer Praxis Books. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72943-3_14
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