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A classification of the second order degenerate elliptic operators and its probabilistic characterization. (English) Zbl 0326.60097

MSC:
60J60 Diffusion processes
35J15 Second-order elliptic equations
58J99 Partial differential equations on manifolds; differential operators
35K10 Second-order parabolic equations
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[1] Blagove??enskii, Iu. N., Freidlin, M.I.: Some properties of diffusion processes depending on a parameter. DAN 138 (1961)
[2] Bony, J.M.: Principe du maximum, unicité du problème de Cauchy et inégalité de Harnack des operateurs elliptiques dégéneres. Ann. Inst. Fourier 19, I, 277-304 (1969) · Zbl 0176.09703
[3] Bucy, R.S., Joseph, P.D.: Filtering for stochastic processes with applications to guidance. New York: Wiley 1968 · Zbl 0174.21903
[4] Duflo, M., Revuz, D.: Propriétés asymptotiques des probabilités de transition des processus de Markov recurrents. Ann. Inst. Henri Poincare, Sec. B. 5 233-244 (1969) · Zbl 0183.47003
[5] Hörmander, L.: Hypoelliptic second order differential equations. Acta Math. 119, 147-171 (1967) · Zbl 0156.10701
[6] ItÔ, K.: Brownian motions on a Lie group. Proc. Japan Acad. 26, 4-10 (1950) · Zbl 0041.45703
[7] ItÔ, K., McKean, H.: Diffusion processes and their sample paths. New York: Academic Press 1964 · Zbl 0837.60001
[8] Kunita, H.: Asymptotic behavior of the nonlinear filtering errors of Markov processes, J. Multi-variate Anal. 1, 365-393 (1971)
[9] Nagano, T.: Linear differential systems with singularities and an application to transitive Lie algebra. J. Math. Soc. Japan 18, 398-404 (1966) · Zbl 0147.23502
[10] Narashimhan, R.: Analysis on real and complex manifolds. Paris: Masson 1968
[11] McKean, H.: Stochastic integrals. New York: Academic Press 1969 · Zbl 0191.46603
[12] Spanier, E.H.: Algebraic topology. New York: McGraw Hill 1966 · Zbl 0145.43303
[13] Stroock, D.W., Varadhan, S.R.S.: On the support of diffusion processes with applications to the strong maximum principle, Proc. 6-th Berkeley Sympos. Math. Statist. Probab. · Zbl 1316.60123
[14] Sussmann, H.J., Jurdjevic, V.: Controllability of nonlinear systems. J. Differential Equations 12, 95-116 (1972) · Zbl 0242.49040
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