Exit times for a class of random walks: exact distribution results: Exit times for random walks

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

SN - 0021-9002

VL - 48A

SP - 51

EP - 63

JO - Journal of Applied Probability

JF - Journal of Applied Probability

ER -