TY - JOUR
T1 - Hypo-exponential distributions and compound Poisson processes with alternating parameters
AU - Ratanov, Nikita
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - Point processes with alternating arrival rates arise in various applications, including financial modelling. We obtain explicit expressions for the distributions of these processes, i.e. for the sums ∑m=1nX(m) and ∑m=1n(-1)mX(m), where X(m) are independent exponentially distributed random variables with alternating parameters. The distribution of the compound Poisson process with Markov modulation and with exponentially distributed jumps is also studied.
AB - Point processes with alternating arrival rates arise in various applications, including financial modelling. We obtain explicit expressions for the distributions of these processes, i.e. for the sums ∑m=1nX(m) and ∑m=1n(-1)mX(m), where X(m) are independent exponentially distributed random variables with alternating parameters. The distribution of the compound Poisson process with Markov modulation and with exponentially distributed jumps is also studied.
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U2 - 10.1016/j.spl.2015.08.006
DO - 10.1016/j.spl.2015.08.006
M3 - Article
AN - SCOPUS:84940029131
SN - 0167-7152
VL - 107
SP - 71
EP - 78
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -