A Stochastic Representation for Nonlocal Parabolic PDEs with Applications

References

• [1] Adams AT, Clunie JB (2006) Risk assessment techniques for split capital investment trusts. Ann. Actuarial Sci. 1(1):7–36.Crossref, Google Scholar
• [2] Bayraktar E, Xing H (2010) On the uniqueness of classical solutions of Cauchy problems. Proc. Amer. Math. Soc. 138(6):2061–2064.Crossref, Google Scholar
• [3] Cadenillas A, Lakner P, Pinedo M (2010) Optimal control of a mean-reverting inventory. Oper. Res. 58(6):1697–1710.Link, Google Scholar
• [4] Chabrowski J (1984a) On nonlocal problems for parabolic equations. Nagoya Math. J. 93:109–131.Crossref, Google Scholar
• [5] Chabrowski J (1984b) On the nonlocal problem with a functional for parabolic equation. Funkcialaj Ekvacioj 27(1):101–123.Google Scholar
• [6] Day WA (1982) Extensions of a property of the heat equation to linear thermoelasticity and other theories. Quart. Appl. Math. 40(3):319–330.Crossref, Google Scholar
• [7] Deng K (1993) Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions. J. Math. Anal. Appl. 179(2):630–637.Crossref, Google Scholar
• [8] Freidlin MI (1985) Functional Integration and Partial Differential Equations (Princeton University Press, Princeton, NJ).Google Scholar
• [9] Friedman A (1986) Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions. Quart. Appl. Math. 44(3):401–407.Crossref, Google Scholar
• [10] Friedman A (2012) Stochastic Differential Equations and Applications (Dover Publications, Mineola, NY).Google Scholar
• [11] Friedman A (2013) Partial Differential Equations of Parabolic Type (Dover Publications, Mineola, NY).Google Scholar
• [12] Glasserman P, Kou SG (1995) Limits of first passage times to rare sets in regenerative processes. Ann. Appl. Probab. 5(2):424–445.Crossref, Google Scholar
• [13] Grigorescu I, Kang M (2013) Markov processes with redistribution. Markov Processes and Related Fields 19(3):497–520.Google Scholar
• [14] Harrison JM, Sellke TM (1983) Impulse control of Brownian motion. Math. Oper. Res. 8(3):454–466.Link, Google Scholar
• [15] Ingersoll JE (1976) A theoretical and empirical investigation of the dual purpose funds: An application of contingent-claims analysis. J. Financial Econom. 3(1):83–123.Crossref, Google Scholar
• [16] Jarrow RA, O’Hara M (1989) Primes and scores: An essay on market imperfections. J. Finance 44(5):1263–1287.Crossref, Google Scholar
• [17] Lieberman GM (1999) Time-periodic solutions of linear parabolic differential equations. Comm. Partial Differential Equations 24(3–4):631–663.Crossref, Google Scholar
• [18] Olmstead WE, Roberts CA (1997) The one-dimensional heat equation with a nonlocal initial condition. Appl. Math. Lett. 10(3):89–94.Crossref, Google Scholar
• [19] Pao CV (1995a) Dynamics of reaction-diffusion equations with nonlocal boundary conditions. Quart. Appl. Math. 3(1):173–186.Crossref, Google Scholar
• [20] Pao CV (1995b) Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions. J. Math. Anal. Appl. 195(3):702–718.Crossref, Google Scholar
• [21] Pao CV (1998) Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boundary conditions. J. Comput. Appl. Math. 88(1):225–238.Crossref, Google Scholar
• [22] Sigman K, Wolff RW (1993) A review of regenerative processes. SIAM Rev. 35(2):269–288.Crossref, Google Scholar
• [23] Yin YF (1994) On nonlinear parabolic equations with nonlocal boundary condition. J. Math. Anal. Appl. 185(1):161–174.Crossref, Google Scholar