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AUTHOR(S): Mario Lefebvre
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TITLE Exit Times and Places for a Wiener Process with Sign-dependent Exponential Jumps |
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ABSTRACT We consider a one-dimensional jump-diffusion process {X(t), t ≥ 0} whose continuous part is a Wiener process with zero drift. The jumps are exponential and depend on the sign of X(t). Let τ (x) be the first time that the process, starting from X(0) = x, is equal to zero, or |X(t)| = d. We obtain exact analytical expressions for the moment-generating function of τ (x), its mean, and the probability that X(τ (x)) = 0. To do so, we solve integro-differential equations, subject to the appropriate boundary conditions. |
KEYWORDS Hitting time, Brownian motion, Poisson process, jump size, integro-differential equation |
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Cite this paper Mario Lefebvre. (2025) Exit Times and Places for a Wiener Process with Sign-dependent Exponential Jumps. International Journal of Education and Learning Systems, 10, 1-5 |
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