AN EXAMPLE OF A STOCHASTIC DIFFERENTIAL EQUATION WITH THE PROPERTY OF WEAK NON-UNIQUENESS OF A SOLUTION

BOGDAN I. KOPYTKO AND MYKOLA I. PORTENKO

Theory of Stochastic Processes Vol. 12 (28), no. 1–2, 2006, pp. 68–76

A family of one-dimensional diffusion processes is constructed such that each one of this family is a weak solution to some stochastic differential equation. It turns out that the property of weak uniqueness of a solution to this equation is failed.

Full version