On the Diameter of the Stopped Spider Process

Published Online:https://doi.org/10.1287/moor.2023.1359

References

  • [1] Atar R, Cohen A (2019) Serve the shortest queue and Walsh Brownian motion. Ann. Appl. Probab. 29(1):613–651.CrossrefGoogle Scholar
  • [2] Barlow M, Pitman J, Yor M (1989) On Walsh’s Brownian motions. Azéma J, Yor M, Meyer PA, eds. Séminaire de Probabilités XXIII, Lecture Notes in Mathematics, vol. 1372 (Springer, Berlin), 275–293.CrossrefGoogle Scholar
  • [3] Baxter JR, Chacon RV (1984) The equivalence of diffusions on networks to Brownian motion. Contemporary Math. 26:33–47.CrossrefGoogle Scholar
  • [4] Dubins LE, Schwarz G (1988) A sharp inequality for submartingales and stopping times. Asterisque 157(158):129–145.Google Scholar
  • [5] Dubins LE, Gilat D, Meilijson I (2009) On the expected diameter of an L2-bounded martingale. Ann. Probab. 37(1):393–402.CrossrefGoogle Scholar
  • [6] Ernst PA (2016) Exercising control when confronted by a (Brownian) spider. Oper. Res. Lett. 44:487–490.CrossrefGoogle Scholar
  • [7] Gilat D, Meilijson I, Sacerdote L (2018) A sharp bound on the expected number of upcrossings of an L2-bounded martingale. Stochastic Processes Their Appl. 128(6):1849–1856.CrossrefGoogle Scholar
  • [8] Gilat D, Meilijson I, Sacerdote L (2022) A note on the maximal expected local time of L2-bounded martingales. J. Theoret. Probab. 35:1952–1965.CrossrefGoogle Scholar
  • [9] Harrison JM, Shepp LA (1981) On skew Brownian motion. Ann. Probab. 9(2):309–313.CrossrefGoogle Scholar
  • [10] Karr AF (1984) The martingale method: Introductory sketch and access to the literature. Oper. Res. Lett. 3(2):59–63.CrossrefGoogle Scholar
  • [11] Meilijson I (2003) The time to a given drawdown in Brownian Motion. Azéma J, Émery M, Ledoux M, Yor M, eds. Séminaire de Probabilités XXXVII, Lecture Notes in Mathematics, vol. 1832 (Springer, Berlin), 94–108.CrossrefGoogle Scholar
  • [12] Peskir G, Shiryaev A (2006) Optimal Stopping and Free-Boundary Problems, Lectures in Mathematics, ETH Zürich (Birkhäuser, Basel, Switzerland).Google Scholar
  • [13] Revuz D, Yor M (2013) Continuous Martingales and Brownian Motion, 3rd ed. (Springer-Verlag, Berlin).Google Scholar
  • [14] Rhee WT, Talagrand M (1987) Martingale inequalities and NP-complete problems. Math. Oper. Res. 12(1):177–181.LinkGoogle Scholar
  • [15] Rhee WT, Talagrand M (1989) Martingale inequalities, interpolation and NP-complete problems. Math. Oper. Res. 14(1):91–96.LinkGoogle Scholar
  • [16] Rogers LCG (1983) Itô excursion theory via resolvents. Zeitschrift Wahrscheinlichkeitstheorie Verwandte Gebiete 63:237–255.CrossrefGoogle Scholar
  • [17] Salisbury TS (1986) Construction of right processes from excursions. Probab. Theory Related Fields 73:351–367.CrossrefGoogle Scholar
  • [18] Walsh JB (1978) A diffusion with a discontinuous local time. Asterisque 52:37–45.Google Scholar
  • [19] Wang G (1991) Sharp maximal inequalities for conditionally symmetric martingales and Brownian motion. Proc. Amer. Math. Soc. 112(2):579–586.CrossrefGoogle Scholar
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