Download this PDF file Fullscreen Fullscreen Off
References
- Atar, R. and Budhiraja, A. Stability properties of constrained jump-diffusion processes. Electronic J. Prob., 7 (2002), paper no. 22, 1--31. Math. Review 2004j:60168
- Berman, A. and Plemmons, R. J. Nonnegative Matrices in the Mathematical Sciences. Classics in Applied Mathematics, Vol. 9 (1994). Society for Industrial and Applied Mathematics (SIAM), Philadelphia.
- Billingsley, P. Convergence of Probability Measures, 2nd. edition. Wiley Series in Probability and Statistics (1999). John Wiley & Sons, Inc., New York.
- Chen, H. and Yao, D. D. Fundamentals of Queueing Networks. Applications of Mathematics, Vol. 46 (2001). Springer-Verlag, New York.
- Dupuis, P. and Ishii, H. On oblique derivative problems for fully nonlinear second order elliptic PDEs on domains with corners. Hokkaido Math. J., 20 (1991), 135--164. Math. Review 92b:35060
- Dupuis, P. and Ishii, H. SDEs with oblique re ection on nonsmooth domains. Ann. Prob., 21 (1993), 554--580. Math. Review 94c:60128
- Ethier, S. N. and Kurtz, T. G. Markov Processes: Characterization and Convergence. Wiley Series in Probability and Statistics (1986). John Wiley & Sons, Inc., New Jersey.
- Harrison, J. M. and Reiman, M. I. Re flected Brownian motion in an orthant. Ann. Prob., 9 (1981), 302--308. Math. Review 82c:60141
- Kallenberg, O. Foundations of Modern Probability, 2nd. edition. Probability and its Applications (2002). Springer-Verlag, New York.
- Karatzas, I. and Shreve, S. E. Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, Vol. 113 (1991). Springer-Verlag, New York.
- Kella, O. and Whitt, W. Diffusion approximations for queues with server vacations. Adv. Appl. Prob., 22 (1990), 706--729. Math. Review 91m:60170
- Kushner, H. J. Approximation and Weak Convergence Methods for Random Processes. The MIT Press, Massachusetts (1984).
- Kushner, H. J. Heavy Traffic Analysis of Controlled Queueing and Communication Networks. Applications of Mathematics, Vol. 47 (2001). Springer- Verlag, New York.
- Mandelbaum, A. and Pats, G. State-dependent stochastic networks. Part I: Approximations and applications with continuous diffusion limits. Ann. Appl. Prob., 8 (1998), 569--646. Math. Review 2000b:60088
- Oksendal, B. Stochastic Differential Equations, 5th. edition. Springer-Verlag, Berlin (2000).
- Oksendal, B. and Sulem, A. Applied Stochastic Control of Jump Diffusions. Springer-Verlag, New York (2005).
- Piera, F., Mazumdar, R., and Guillemin, F. On product-form stationary distributions for re flected diffusions with jumps in the positive orthant. Adv. Appl. Prob., 37 (2005), 212--228. Math. Review 2006e:60116
- Piera, F., Mazumdar, R., and Guillemin, F. On the local times and boundary properties of reflected diffusions with jumps in the positive orthant. Markov Processes Rel. Fields, 12 (2006), 561--582. Math. Review 2007j:60125
- Piera, F., Mazumdar, R., and Guillemin, F. Boundary behavior and product-form stationary distributions of jump-diffusions in the orthant with state-dependent re flections. Adv. Appl. Prob., 40 (2008), 529--547. Math. Review 2433708
- Protter, P. Stochastic Integration and Differential Equations, 2nd. edition. Applications of Mathematics, Vol. 21 (2004). Springer-Verlag, Berlin.
- Ramasubramanian, S. A subsidy-surplus model and the Skorokhod problem in an orthant. Math. Oper. Res., 25 (2000), 509--538. Math. Review 2002g:91107
- Revuz, D. and Yor, M. Continuous Martingales and Brownian Motion, 3rd. (corrected third printing) ed. A Series of Comprehensive Studies in Mathematics, Vol. 293 (2005). Springer-Verlag, Berlin.
- Rong, S. Refl ecting Stochastic Differential Equations with Jumps and Applications. Research Notes in Mathematics, Vol. 408 (2000). Chapman and Hall/CRC, London.
- Shashiashvili, M. A lemma of variational distance between maximal functions with application to the Skorokhod problem in a nonnegative orthant with state-dependent re flection directions. Stochastics Stochastics Rep., 48 (1994), 161--194. Math. Review 2001e:60173
- Whitt, W. The refl ection map with discontinuities. Math. Oper. Res., 26 (2001), 447--484. Math. Review 2002f:90009
- Whitt, W. Stochastic-Process Limits. Springer Series in Operations Research (2002). Springer-Verlag, New York.

This work is licensed under a Creative Commons Attribution 3.0 License.