000			03429cam a2200409 i 4500
001			on1389609253
003			OCoLC
005			20241127152807.0
008			230709t20232023sz a b 001 0 eng d
015			_aGBC3J0472 _2bnb
016	7		_a021235255 _2Uk
020			_a303141019X _q(paperback)
020			_a9783031410192 _q(paperback)
029	1		_aUKMGB _b021235255
029	1		_aAU@ _b000075540308
035			_a(OCoLC)1389609253
040			_aYDX _beng _erda _cYDX _dBDX _dUKMGB _dXII _dOHX _dQGJ _dOCLCO _dWAU _dFUG _dOCLCO _dPAU
082	0	4	_a519.282
100	1		_aUchiyama, Kôhei, _eauthor.
245	1	0	_aPotential functions of random walks in Z with infinite variance : _bestimates and applications / _cKôhei Uchiyama.
264		1	_aCham, Switzerland : _bSpringer, _c[2023]
264		4	_c©2023
300			_aix, 276 pages ; _c24 cm.
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aLecture notes in mathematics, _x0075-8434 ; _vvolume 2338
504			_aIncludes bibliographical references (pages 269-272) and indexes.
520	3		_a"This book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, yielding precise asymptotic results on, among other things, hitting probabilities of finite sets, overshoot distributions, Green functions on long finite intervals and the half-line, and absorption probabilities of two-sided exit problems. The potential function of a random walk is a central object in fluctuation theory. If the variance of the step distribution is finite, the potential function has a simple asymptotic form, which enables the theory of recurrent random walks to be described in a unified way with rather explicit formulae. On the other hand, if the variance is infinite, the potential function behaves in a wide range of ways depending on the step distribution, which the asymptotic behaviour of many functionals of the random walk closely reflects. In the case when the step distribution is attracted to a strictly stable law, aspects of the random walk have been intensively studied and remarkable results have been established by many authors. However, these results generally do not involve the potential function, and important questions still need to be answered. In the case where the random walk is relatively stable, or if one tail of the step distribution is negligible in comparison to the other on average, there has been much less work. Some of these unsettled problems have scarcely been addressed in the last half-century. As revealed in this treatise, the potential function often turns out to play a significant role in their resolution. Aimed at advanced graduate students specialising in probability theory, this book will also be of interest to researchers and engineers working with random walks and stochastic systems."-- _cBack cover.
650		0	_aRandom walks (Mathematics)
650		6	_aMarches aléatoires (Mathématiques)
830		0	_aLecture notes in mathematics (Springer-Verlag) ; _v2338. _x0075-8434
942			_2ddc _cBK _n0
948			_hNO HOLDINGS IN P5A - 36 OTHER HOLDINGS
999			_c41626 _d41626