ONE EXAMPLE OF A RANDOM CHANGE OF TIME THAT TRANSFORMS A GENERALIZED DIFFUSION PROCESS INTO AN ORDINARY ONE

OLGA V. ARYASOVA AND MYKOLA I. PORTENKO

Theory of Stochastic Processes Vol. 13 (29), no. 3, 2007, pp. 12–21

We propose a random change of time for a class of generalized diffusion processes such that the corresponding stochastic differential equation (with generalized coefficients) is transformed into an ordinary one (its coefficients are some non-generalized functions). It turns out that the latter stochastic differential equation has no property of the (weak) uniqueness of a solution.

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