The quadratic variation of a Poisson process N(t) is[N,N](t) = N(t) by XXXXXXXXXXand the expression of - dN in Example 4.4. See also Example 3.52.Let X(t) be a real-valued process defined by the...

The quadratic variation of a Poisson process N(t) is[N,N](t) = N(t) by (4.27) and the expression of - dN in Example 4.4. See also Example 3.52.Let X(t) be a real-valued process defined by the stochastic differential equation dX(t) = sign(X(t)) dB(t), t = 0, where X(0) = 0, B is a Brownian motion starting at zero, and sign(x) = -1, 0, and 1 for x 0, respectively. This equation has a weak solution ([3], Sect. 7.3) that is unique in the weak sense ([3], pp. 248–249) but it is not unique in the strong sense.