Том 69
№ 9

All Issues

On Multidimensional Generalized Diffusion Processes

Shevchenko H. M.

Full text (.pdf)


We construct a multidimensional generalized diffusion process with the drift coefficient that is the (generalized) derivative of a vector-valued measure satisfying an analog of the Hölder condition with respect to volume. We prove the existence and continuity of the density of transition probability of this process and obtain standard estimates for this density. We also prove that the trajectories of the process are solutions of a stochastic differential equation.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 9, pp 1560-1566.

Citation Example: Shevchenko H. M. On Multidimensional Generalized Diffusion Processes // Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1291-1296.

Full text