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Aronson, D.G. Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967), 890–896.
Borell, C. Convex measures on locally convex spaces, Ark. Mat. 12 (1974), 239–252.
Borell, C. Greenian potentials and concavity, Math. Ann. 272, (1985), 155–160.
Cafarelli, L.A.; Friedman, A. Convexity of solutions of semilinear elliptic equations, Duke Math. J. 52 (1985), 431–456.
Cafarelli, L.A.; Spruck, J. Convexity properties of solutions to some classical variational problems, Comm. Partial Differential Equations 7 (1982), 1337–1379.
Davidovič, Ju.S.; Korenbljum, B.I; Hacet, I. A property of logarithmically concave functions, Soviet Math. Dokl. 10 (1969), 477–480.
Hajek, B. Mean stochastic comparison of diffusions, Z. Wahrsch. Verw. Gebiete 68 (1985), 315–329.
Ikeda, N.; Watanabe, S. A comparison theorem for solutions of stochastic differential equations and its applications, Osaka J. Math. 14 (1977), 619–633.
Korevaar, N.J. Convex solutions to nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. 32 (1983), 603–614.
Kröger, P. Vergleichssätze für Diffunsionsprozesse, Thesis Erlangen (1986).
Kröger, P. Comparison de diffusions, C.R. Acad. Sci. Paris Sér.I 305 (1987), 89–92.
Krylov, N.V. Safonov, M.V. A certain property of solutions of parabolic equations with measurable coefficients, Math. USSR-Izv. 16 (1981), 151–164.
Lions, P.L. Two geometrical properties of solutions of semilinear problems. Applicable Anal. 12 (1981), 267–272.
Nickel, K. Gestaltaussagen über Lösungen parabolischer Differentialgleichungen, J. Reine Angew. Math. 211 (1962), 78–94.
Phillips, R.S. Perturbation theory for semigroups of linear operators, Trans. Amer. Math. Soc. 74 (1953), 199–221.
Skorochod, A.V. Existence and uniqueness of solutions to stochastic diffusion equations (russian), Sibirsk Mat. Zh. 2 (1961), 129–137.
Stroock, D.W. Varadhan, S.R.S. Multidimensional diffusion processes, Springer Berlin 1979.
Walter, W. Differential and integral inequalities, Springer Berlin 1970.
Yamada, T. On a comparison theorem for solutions of stochastic differential equations and its applications, J. Math. Kyoto Univ. 13 (1973), 497–512.
Yamada, T. On the non-confluent property of solutions of one-dimensional stochastic differential equations, Stochastics 17 (1986), 111–124.
Yamada, T.; Ogura, Y. On the strong comparison theorem for solutions of stochastic differential equations, Z. Wahrsch. Verw. Gebiete 56 (1985), 3–19.
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© 1989 Springer-Verlag
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Kröger, P. (1989). Invariance of cones and comparison results for some classes of diffusion processes. In: Christopeit, N., Helmes, K., Kohlmann, M. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043783
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DOI: https://doi.org/10.1007/BFb0043783
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