dc.contributor.author Kovats, Jay ( ) dc.date.accessioned 2020-11-25T21:02:36Z dc.date.available 2020-11-25T21:02:36Z dc.date.issued 2003-07-13 dc.identifier.citation Kovats, J. (2003). The Kolmogorov equation with time-measurable coefficients. Electronic Journal of Differential Equations, 2003(77), pp. 1-14. en_US dc.identifier.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/13017 dc.description.abstract Using both probabilistic and classical analytic techniques, we investigate the parabolic Kolmogorov equation `Ltv + ∂v/ ∂t ≡ 1/2αij (t)vxixj + bi(t)vxi - c(t)v + ƒ(t) + ∂v/ ∂t = 0` in HT : = (0, T) x Ed and its solutions when the coefficients are bounded Borel measurable functions of t. We show that the probabilistic solution v(t, x) defined in ĦT, is twice differentiable with respect to x, continuously in (t, x), once differentiable with respect to t, a.e. t ∈ [0, T) and satisfies the Kolmogorov equation Ltv + ∂v/ ∂t = 0 a.e. in ĦT. Our main tool will be the Aleksandrov-Busemann-Feller Theorem. We also examine the probabilistic solution to the fully nonlinear Bellman equation with time-measurable coefficients in the simple case b ≡ 0, c ≡ 0. We show that when the terminal data function is a paraboloid, the payoff function has a particularly simple form. en_US dc.format Text dc.format.extent 14 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Southwest Texas State University, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. dc.subject Diffusion processes en_US dc.subject Kolmogorov equation en_US dc.subject Bellman equation en_US dc.title The Kolmogorov equation with time-measurable coefficients en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License.
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