Geodesic
Formula for the Laplace Transform of the Projection of a Distribution on the Positive Semiaxis and Some of Its Applications
Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 741-754.

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We obtain a formula for the Laplace transform of the restriction of an arbitrary probability distribution on the positive semiaxis in the form of a Cauchy-type integral in infinite limits of the characteristic function of this distribution. Using this result and the estimates of the concentration function of the sum of independent random variables, we derive a representation for the Laplace transform of the restriction of the harmonic measure on the positive semiaxis. In conclusion, we present an estimate of the lower ladder height distribution for the case in which the distribution of the value of the jump in a random walk is normal.
Mots-clés : Laplace transform
Keywords: probability distribution, Cauchy integral, harmonic measure, renewal measure, random walk, Vitali theorem. 
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S. V. Nagaev. Formula for the Laplace Transform of the Projection of a Distribution on the Positive Semiaxis and Some of Its Applications. Matematičeskie zametki, Tome 84 (2008) no. 5, pp. 741-754. http://geodesic.mathdoc.fr/item/MZM_2008_84_5_a9/

[1] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, M., 1984 | MR | Zbl

[2] V. M. Zolotarev, “Preobrazovanie Mellina–Stiltesa v teorii veroyatnostei”, Teoriya veroyatn. i ee primen., 2:4 (1957), 444–469 | MR

[3] S. V. Nagaev, S. S. Khodzhabagyan, “Ob otsenke funktsii kontsentratsii summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 41:3 (1996), 655–665 | MR | Zbl

[4] P. Greenwood, E. Omey, J. L. Teugels, “Harmonic renewal measures”, Z. Wahrsch. Verw. Gebiete, 59:3 (1982), 391–409 | DOI | MR | Zbl

[5] P. Greenwood, E. Omey, J. L. Teugels, “Harmonic renewal measures and bivariate domains of attractions in fluctuation theory”, Z. Wahrsch. Verw. Gebiete, 61:4 (1982), 527–539 | DOI | MR | Zbl

[6] R. Grübel, “On harmonic renewal measures”, Probab. Theory Relat. Fields, 71:3 (1986), 393–404 | DOI | MR | Zbl

[7] R. J. Grübel, “Harmonic renewal sequences and the first positive sum”, J. London Math. Soc. (2), 38:1 (1988), 179–192 | DOI | MR | Zbl

[8] A. J. Stam, “Some theorems on harmonic renewal measures”, Stochastic Process. Appl., 39:2 (1991), 277–285 | DOI | MR | Zbl

[9] A. V. Nagaev, “Ob odnom sposobe vychisleniya momentov lestnichnoi vysoty”, Teoriya veroyatn. i ee primen., 30:3 (1985), 535–538 | MR | Zbl

[10] I. P. Natanson, Teoriya funktsii veschestvennoi peremennoi, GIFML, M., 1957 | MR | Zbl

[11] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya, t. 2, GIFML, M., 1959 | MR | Zbl

[12] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1963 | MR | Zbl