Exit times for a class of random walks: exact distribution results: Exit times for random walks
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Exit times for a class of random walks: exact distribution results : Exit times for random walks. / Jacobsen, Martin.
I: Journal of Applied Probability, Bind 48A, 2011, s. 51-63.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Exit times for a class of random walks: exact distribution results
T2 - Exit times for random walks
AU - Jacobsen, Martin
N1 - Special issue. New Frontiers in Applied Probability : A Festschrift for Søren Asmussen. (Ed. by P. Glynn, T. Mikosch and T. Rolski)
PY - 2011
Y1 - 2011
N2 - For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its generating function, when assuming that the distribution of the jump in the direction making the exit possible has a Laplace transform which is a rational function. The expected exit time is also determined and the paper concludes with exact distribution results concerning exits from bounded intervals. The proofs use simple martingale techniques together with some classical expansions of polynomials and Rouché's theorem from complex function theory.
AB - For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its generating function, when assuming that the distribution of the jump in the direction making the exit possible has a Laplace transform which is a rational function. The expected exit time is also determined and the paper concludes with exact distribution results concerning exits from bounded intervals. The proofs use simple martingale techniques together with some classical expansions of polynomials and Rouché's theorem from complex function theory.
M3 - Journal article
VL - 48A
SP - 51
EP - 63
JO - Journal of Applied Probability
JF - Journal of Applied Probability
SN - 0021-9002
ER -
ID: 109661089