Abstract
The Fokker–Planck–Kolmogorov parabolic second-order differential operator is considered, for which its fundamental solution is derived in explicit form. Such operators arise in numerous applications, including signal filtering, portfolio control in financial mathematics, plasma physics, and problems involving linear-quadratic regulators.
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References
R. Cordero-Soto, R. M. Lopez, E. Suazo, and S. K. Suslov, Lett. Math. Phys. 84 (2–3), 159–178 (2008).
S. S.-T. Yau, Q. Appl. Math. 62 (4), 643–650 (2004).
C. F. F. Karney, Comput. Phys. Rep. 4 (3–4), 183–244 (1986).
G. D. Kerbel and M. G. McCoy, Phys. Fluids 28, 3629–3649 (1985).
A. I. Ovseevich, Probl. Inf. Transmission 44 (1), 53–71 (2008).
A. G. Chechkin, J. Math. Sci. 210 (4), 545–555 (2015).
W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control (Springer-Verlag, Berlin, 1975; Mir, Moscow, 1978).
J. J. Levin, Proc. Am. Math. Soc. 10 (4), 519–524 (1959).
P. Lancaster and L. Rodman, Algebraic Riccati Equations (Clarendon, Oxford, 1995).
H. Abou-Kandil, G. Freiling, V. Ionescu, and G. Jank, Matrix Riccati Equations in Control and Systems Theory (Birkhäuser, Basel, 2003).
S. M. Nikol’skii, A Course in Calculus, 3rd ed. (Nauka, Moscow, 1983) [in Russian].
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Original Russian Text © A.G. Chechkin, A.S. Shamaev, 2017, published in Doklady Akademii Nauk, 2017, Vol. 472, No. 4, pp. 383–387.
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Chechkin, A.G., Shamaev, A.S. On the fundamental solution of the Fokker–Planck–Kolmogorov equation. Dokl. Math. 95, 55–59 (2017). https://doi.org/10.1134/S1064562417010161
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DOI: https://doi.org/10.1134/S1064562417010161