Functional Limit Theorems for a Simple Auction

References

• Billingsley P.Probability and Measure (1986) 2nd ed.(Wiley, New York) Google Scholar
• Billingsley P.Convergence of Probability Measures (1999) 2nd ed.(Wiley, New York) Crossref, Google Scholar
• Bramson M. Convergence to equilibria for fluid models of FIFO queueing networks. Queueing Systems. Theory Appl. (1996a) 22:5–45Crossref, Google Scholar
• Bramson M. Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks. Queueing Systems. Theory Appl. (1996b) 23:1–26Crossref, Google Scholar
• Bramson M. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems. Theory Appl. (1998) 30:89–148Crossref, Google Scholar
• Doytchinov B., Lehoczky J. P., Shreve S. E. Real-time queues in heavy traffic with earliest-deadline-first queue discipline. Ann. Appl. Probability (2001) 11:332–378Crossref, Google Scholar
• Dupuis P., Ishii H. On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics Stochastics Rep. (1991) 35:31–62Crossref, Google Scholar
• Ethier S. N., Kurtz T. G.Markov Processes: Characterization and Convergence (1985) (Wiley, New York) Google Scholar
• Gromoll H. C. Diffusion approximation for a processor sharing queue in heavy traffic. Ann. Appl. Probab. (2003) . ForthcomingGoogle Scholar
• Kruk Ł., Lehoczky J. P., Shreve S. E., Yeung S-N. Multiple-input heavy-traffic real-time queues. Ann. Appl. Probab. (2003) 13:54–99Crossref, Google Scholar
• O'Hara M.Market Microstructure Theory (1995) (Blackwell Publishers, Cambridge, MA) Google Scholar
• Pagano M., Roell A. Transparency and liquidity: A comparison of auction and dealer markets with informed trading. J. Finance (1996) 51:579–611Crossref, Google Scholar
• Peterson W. P. A heavy traffic limit theorem for networks of queues with multiple customer types. Math. Oper. Res. (1991) 16:90–118Link, Google Scholar
• Prokhorov Yu. Convergence of random processes and limit theorems in probability theory. Theory Probability Appl. (1956) 1:157–214Crossref, Google Scholar
• Reiman M. I., Williams R. J. A boundary property of semimartingale reflected Brownian motions. Probab. Theory Related Fields (1988/1989) 77-80:87-633–97Google Scholar
• Taylor L. M., Williams R. J. Existence and uniqueness of semimartingale reflected Brownian motions in an orthant. Probab. Theory Related Fields (1993) 96:283–317Crossref, Google Scholar
• Wheeden R. L., Zygmund A.Measure and Integral: An Introduction to Real Analysis (1977) (Marcel Dekker, New York) Crossref, Google Scholar
• Williams R. J. An invariance principle for semimartingale reflecting Brownian motion in an orthant. Queueing Systems. Theory Appl. (1998a) 30:5–25Crossref, Google Scholar
• Williams R. J. Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse. Queueing Systems. Theory Appl. (1998b) 30:27–88Crossref, Google Scholar