A closer look at the solutions of a degenerate stochastic differential equation (Q2891104)

After a discussion of known results on the stochastic differential equation NEWLINE\[NEWLINEX_t=X_0 +\int^t _0 \sigma(X_s)\, dB_s +\int^t _0 b(X_s)\,ds, \;\; t\geq 0,NEWLINE\]NEWLINE the authors turn their attention to a careful examination of the Tanaka SDE NEWLINE\[NEWLINEX_t =\int^t _0 \text{sgn}(X_s)\, dB_s,\;\;\;t\geq 0.NEWLINE\]NEWLINE The explicit form of all weak solutions of this equation are found, while the main result shows why strong solutions neither exist nor are unique.