Geodesic
Inequalities for Bessel functions of imaginary argument
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 525-530

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Using probabilistic arguments (the method of conjugate distributions and a local limit theorem), we prove two-sided inequality (9) for modified Bessel functions $I_n(z)$ with integer $n\ge0$. The inequalities obtained are very useful, for example, in estimation of probabilities of large deviations in spaces of high dimensionality. 
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     author = {A. V. Prokhorov},
     title = {Inequalities for {Bessel} functions of imaginary argument},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {525--530},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a15/}
}
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A. V. Prokhorov. Inequalities for Bessel functions of imaginary argument. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 3, pp. 525-530. http://geodesic.mathdoc.fr/item/TVP_1968_13_3_a15/