The expected time to end the tug-of-war in a wedge

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• 作者：Dante DeBlassie (1)
  Robert G. Smits (1)
  
• 关键词：Tug ; of ; war ; Wedge ; p ; Harmonic functions ; Inhomogeneous game p ; Laplacian ; Expected time to end the game ; Critical angle ; Primary 60G40 ; 60K99 ; 91A15 ; 35J92 ; Secondary 91A24 ; 60G42 ; 35B65 ; 34A34
• 刊名：Probability Theory and Related Fields
• 出版年：2013
• 出版时间：2 - February 2013
• 年：2013
• 卷：155
• 期：1
• 页码：347-378
• 全文大小：291KB
• 参考文献：1. Abdellaoui B., Peral I.: Existence and nonexistence results for quasilinear elliptic equations involving the p-Laplacian with a critical potential. Ann. Mat. Pura Appl. 182, 247鈥?70 (2003) CrossRef
  2. Aronsson G.: Construction of singular solutions to the / p-harmonic equation and its limit equation for / p聽=聽鈭? Manuscr. Math. 56, 135鈥?58 (1986) CrossRef
  3. Ba帽uelos R., DeBlassie R.D., Smits R.G.: The first exit time of planar Brownian motion from the interior of a parabola. Ann. Probab. 29, 882鈥?01 (2001) CrossRef
  4. Ba帽uelos R., Smits R.G.: Brownian motion in cones. Probab. Theory Relat. Fields 108, 299鈥?19 (1997) CrossRef
  5. Bidaut-V茅ron M.-F.: Local and global behaviors of solutions of quasilinear equations of Emden-Fowler type. Arch. Ration. Mech. Anal. 107, 293鈥?24 (1989) CrossRef
  6. Brown B.M., Reichel W.: Eigenvalues of the radially symmetric p-Laplacian in ${\mathbb{R}^n}$ . J. Lond. Math. Soc. 69, 657鈥?75 (2004) CrossRef
  7. Burkholder D.L.: Distribution function inequalities for martingales. Ann. Probab. 1, 19鈥?2 (1973) CrossRef
  8. Burkholder D.L.: Exit times of Brownian motion, harmonic majorization and Hardy spaces. Adv. Math. 26, 182鈥?05 (1977) CrossRef
  9. Coddington E.A., Levinson N.: Theory of Ordinary Differential Equations. McGraw Hill, New York (1955)
  10. Davis B., Zhang B.: Moments of the lifetime of conditioned Brownian motion in cones. Proc. Am. Math. Soc. 121, 925鈥?29 (1994) CrossRef
  11. DeBlassie R.D.: Exit times from cones in ${\mathbb{R}^n}$ of Brownian motion. Probab. Theory Relat. Fields 74, 1鈥?9 (1987) CrossRef
  12. Dr谩bek P.: Nonlinear Eigenvalue problems for the p-Laplacian in ${\mathbb{R}^n}$ . Math. Nachr. 173, 131鈥?39 (1995) CrossRef
  13. Dynkin E.B., Yushkevich A.A.: Markov Processes: Theorems and Problems. Plenum, New York (1969)
  14. Fleckinger J., Man谩sevich R.F., Stavrakakis N.M., de Th茅lin F.: Principal eigenvalues for some quasilinear elliptic equation in ${\mathbb{R}^n}$ . Adv. Differ. Equ. 2, 981鈥?003 (1997)
  15. Fleckinger J., Harrell E.M. II, Stavrakakis N.M., de Th茅lin F.: Boundary behavior and estimates for solutions of equations containing the p-Laplacian. Electron. J. Differ. Equ. 1999(38), 1鈥?9 (1999)
  16. Kakutani S.: Two-dimensional Brownian motion and harmonic functions. Proc. Imp. Acad. Tokyo 20, 706鈥?14 (1944) CrossRef
  17. Krist谩ly A.: An existence result for gradient-type systems with a nondifferentiable term on unbounded strips. J. Math. Anal. Appl. 299, 186鈥?04 (2004) CrossRef
  18. Lazarus, A.J., Loeb, D.E., Propp, J.G., Ullman, D.: Richman games. In: Games of No Chance (Berkeley, CA, 1994), pp. 439鈥?49. Math. Sci. Res. Inst. Publ., vol. 29. Cambridge University Press, Cambridge (1996)
  19. Liskevich V., Lyakhova S., Moroz V.: Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains. J. Differ. Equ. 232, 212鈥?52 (2007) CrossRef
  20. Maitra A., Sudderth W.: Finitely additive stochastic games with Borel measurable payoffs. Int. J. Game Theory 27, 257鈥?67 (1998) CrossRef
  21. Montefusco E., R膬dulescu V.: Nonlinear eigenvalue problems for quasilinear operators on unbounded domains. Nonlinear Differ. Equ. Appl. 8, 481鈥?97 (2001) CrossRef
  22. Panayotounakos D.E.: Exact analytic solutions of unsolvable classes of first and second order nonlinear ODEs (Part I: Abel鈥檚 equations). Appl. Math. Lett. 18, 155鈥?62 (2005) CrossRef
  23. Peres Y., Sheffield S.: Tug-of-war with noise: a game-theoretic view of the / p-Laplacian. Duke Math. J. 145, 91鈥?20 (2008) CrossRef
  24. Peres Y., Schramm O., Sheffield S., Wilson D.B.: Random-turn hex and other selection games. Am. Math. Monthly 114, 373鈥?87 (2007)
  25. Peres Y., Schramm O., Sheffield S., Wilson D.B.: Tug-of-war and the infinity Laplacian. J. Am. Math. Soc. 22, 167鈥?10 (2009) CrossRef
  26. Pfl眉ger K.: Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition. Electron. J. Differ. Equ. 1998(10), 1鈥?3 (1998)
  27. Polyanin A.D., Zaitsev V.F.: Handbook of Exact Solutions for Ordinary Differential Equations, 2nd edn. Chapman & Hall/CRC, Boca Raton (2003)
  28. Spencer J.: Balancing goods. J. Combin. Theory Ser. B 23, 68鈥?4 (1977) CrossRef
  29. Yu L.-S.: Nonlinear p-Laplacian problems on unbounded domains. Proc. Am. Math. Soc. 115, 1037鈥?045 (1992)
  
• 作者单位：Dante DeBlassie (1)
  Robert G. Smits (1)
  
  1. Department of Mathematical Sciences, New Mexico State University, P.O. Box 30001, Department 3MB, Las Cruces, NM, 88003-8001, USA
  
• ISSN：1432-2064

文摘

Using a solution of a nonhomogeneous partial differential equation involving the p-Laplacian, we study the finiteness of the expected time to end the tug-of-war in a wedge.