×

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Blagoveščenskii, 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 (1968), New York: Wiley, New York · 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 (1964), New York: Academic Press, New York · Zbl 0127.09503
[8] Kunita, H., Asymptotic behavior of the nonlinear filtering errors of Markov processes, J. Multi-variate Anal., 1, 365-393 (1971) · Zbl 0245.93027
[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 (1968), Paris: Masson, Paris
[11] McKean, H., Stochastic integrals (1969), New York: Academic Press, New York · Zbl 0191.46603
[12] Spanier, E. H., Algebraic topology (1966), New York: McGraw Hill, New York · 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.