Two-Sided First Exit Problem for Jump Diffusion Processes Having Jumps with a Mixture of Erlang Distribution

Yuzhen Wen; Chuancun Yin
August 2013
Applied Mathematics;Aug2013, Vol. 4 Issue 8, p1142
Academic Journal
In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time


Related Articles

  • On the First-Passage Area of a One-Dimensional Jump-Diffusion Process. Abundo, Mario // Methodology & Computing in Applied Probability;Mar2013, Vol. 15 Issue 1, p85 

    For a one-dimensional jump-diffusion process X( t), starting from x > 0, it is studied the probability distribution of the area A( x) swept out by X( t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A( x) are solutions to certain...

  • Distribution of functionals of bridges for diffusions with jumps. Borodin, A. // Journal of Mathematical Sciences;Dec2007, Vol. 147 Issue 4, p6864 

    The paper deals with a method of calculation of distributions for functionals of bridges of a process which is a generalization of a diffusion with jumps. The approach to calculation of distributions for integral functionals of bridges is the same as for the diffusion itself. This approach is...

  • FIRST EMPTINESS IN THE SPARE PARTS PROBLEM FOR REPARABLE COMPONENTS. Srinivasan, V.S. // Operations Research;Mar/Apr68, Vol. 16 Issue 2, p407 

    This paper investigates the probability distribution of time to first emptiness in the spare parts problem for repairable components, where 'r' spares are provided initially. Two cases are considered, namely, (I) when the component is constantly used, and (ii) when it is intermittently used....

  • Density distribution functions of confined Tonks–Takahashi fluids. Davis, H. Ted // Journal of Chemical Physics;9/15/1990, Vol. 93 Issue 6, p4339 

    The density distribution functions of a confined one-dimensional fluid of particles obeying the Tonks–Takahashi nearest neighbor two-body potential are reduced to simple functions of the grand canonical ensemble partition function. The resulting formulas are analogous to those found by...

  • On a Sparre Andersen Risk Model with Time-Dependent Claim Sizes and Jump-Diffusion Perturbation. Zhang, Zhimin; Yang, Hailiang; Yang, Hu // Methodology & Computing in Applied Probability;Dec2012, Vol. 14 Issue 4, p973 

    In this paper, we consider a Sparre Andersen risk model where the interclaim time and claim size follow some bivariate distribution. Assuming that the risk model is also perturbed by a jump-diffusion process, we study the Gerber-Shiu functions when ruin is due to a claim or the jump-diffusion...

  • THE JOINT LAPLACE TRANSFORMS FOR DIFFUSION OCCUPATION TIMES. BIN LI; XIAOWEN ZHOU // Advances in Applied Probability;Dec2013, Vol. 45 Issue 4, p1049 

    In this paper we adopt the perturbation approach of Landriault, Renaud and Zhou (2011) to find expressions for the joint Laplace transforms of occupation times for time-homogeneous diffusion processes. The expressions are in terms of solutions to the associated differential equations. These...

  • Properties of kagi and renko moments for homogeneous diffusion processes. Spiryaev, M. // Mathematical Notes;Feb2012, Vol. 91 Issue 1/2, p259 

    For a homogeneous diffusion process ( X), we consider problems related to the distribution of the stopping times . The results obtained are used to construct an inductive procedure allowing us to find the distribution of the increments of the process X between two adjacent kagi and renko...

  • Two New Mixture Models: Living With Collinearity but Removing Its Influence. Cornell, John A.; Gorman, John W. // Journal of Quality Technology;Jan2003, Vol. 35 Issue 1, p78 

    Illustrates the benefits of fitting mixture models using numerical collinearity examples. Background to the analysis; Dissolution property of tablets; Discussion of the model forms.

  • A UNIFIED APPROACH TO THE STUDY OF TAIL PROBABILITIES OF COMPOUND DISTRIBUTIONS. Cai, Jun; Garrido, Jose // Journal of Applied Probability;Dec99, Vol. 36 Issue 4, p1058 

    Considers the tail probabilities of a class of compound distributions. Discussion on the relations between reliability distribution classes and heavy-tailed distributions; What the relations reveal; How a generalized Wald's identity and identities for compound geometric distributions are presented.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics