On the Control of the Wienetr Process with Restricted Number of Switchigs

The paper is dealing with random processes which are obtained by switching the drift coefficient of a Wiener process from the value $\beta$ to $-\beta$ and vice-versa. Switching strategies which maximize the expected first exit time from the interval $(-1,1)$ when the expected number of switchings is fixed are examined. Local time is employed in the definition of these strategies.