References
V. M. Borodikhin, “An existence theorem for the two-parameter martingale problem,” in: Abstracts: The First World Congress of the Bernoulli Society for Mathematical Statistics and Probability Theory [in Russian], Nauka, Moscow, 1986,2, p. 652.
D. W. Stroock and S. R. S. Varadhan, “Diffusion processes with continuous coefficients,” Comm. Pure Appl. Math.,22, 345–400 (1969).
C. Tudor, “A theorem concerning the existence of the weak solution of the stochastic equation with continuous coefficients in the plane,” Rev. Roumaine Math. Pures Appl.,22, 1303–1308 (1977).
C. Tudor, “On the existence and the uniqueness of solutions to stochastic integral equations with two-dimensional time parameter,” Rev. Roumaine Math. Pures Appl.,24, 817–827 (1979).
C. Tudor, “An invariance principle for Markov processes with two-dimensional time parameter,” Rev. Roumaine Math. Pures Appl.,24, 1513–1523 (1979).
C. Tudor, “Remarks on the martingale problem in the two-dimensional time parameter,” Rev. Roumaine Math. Pures Appl.,25, 1551–1556 (1980).
C. Tudor, “Stochastic integral equations in the plane,” Rev. Roumaine Math. Pures Appl.,26, 507–538 (1981).
V. M. Borodikhin, “On the martingale problem in the plane,” in: Limit Theorems of Probability Theory and Related Questions [in Russian], Nauka, Novosibirsk, 1982, pp. 146–156.
I. I. Gikhman and T. E. Pyasetskaya, “On a certain class of stochastic partial differential equations with two-parameter white noise,” in: Limit Theorems for Stochastic Processes [in Russian], Kiev, 1977, pp. 71–92.
K. R. Parthasarathy, Probability Measures on Metric Spaces, Acad. Press, New York etc. (1967).
V. M. Borodikhin, “Density conditions for a family of measures in a certain space of two-parameter functions of Lipschitz type,” Sibirsk. Mat. Zh.,31, No. 4, 27–32 (1990).
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Translated from Sibirskii Matemaiicheskii, Vol. 36, No. 2, pp. 248–265, March–April, 1995.
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Borodikhin, V.M. Proof of existence theorems for the two-parameter martingale problem. Sib Math J 36, 219–234 (1995). https://doi.org/10.1007/BF02110145
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DOI: https://doi.org/10.1007/BF02110145