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dc.contributor.authorKovats, Jay ( )
dc.identifier.citationKovats, J. (2003). The Kolmogorov equation with time-measurable coefficients. Electronic Journal of Differential Equations, 2003(77), pp. 1-14.en_US

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.

dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectDiffusion processesen_US
dc.subjectKolmogorov equationen_US
dc.subjectBellman equationen_US
dc.titleThe Kolmogorov equation with time-measurable coefficientsen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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