Duration of stay inside an interval by the poisson process with a negative exponential component

Several two-boundary problems for the Poisson process with an exponential component are solved in the present article. The integral transforms of the joint distribution of the epoch of the first exit from the interval and the value of the overshoot through boundaries at the epoch of the exit are obtained. The Laplace transform of the total duration time of the process’s stay inside the interval is found

Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order kk and beyond

We introduce two classes of point processes: a fractional non-homogeneous Poisson process of order k and a fractional non-homogeneous Pólya-Aeppli process of order k. We characterize these processes by deriving their non-local governing equations. We further study the covariance structure of the processes and investigate the long-range dependence property

Fractional non-homogeneous Poisson and Pólya-Aeppli processes of order k and beyond

We introduce two classes of point processes: a fractional non-homogeneous Poisson process of order k and a fractional non-homogeneous Pólya-Aeppli process of order k: We characterize these processes by deriving their non-local governing equations. We further study the covariance structure of the processes and investigate the long-range dependence property

Valuation Of Continuously Monitored Double Barrier Options And Related Securities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/92059/1/j.1467-9965.2010.00469.x.pd