Suppose Xt is a solution to the one-dimensional SDE Suppose σ and b are bounded and continuous and f is a bounded and continuous function. What ordinary differential equation must H(x) satisfy (in...

Suppose X_t
is a solution to the one-dimensional SDE

Suppose σ and b are bounded and continuous and f is a bounded and continuous function. What ordinary differential equation must H(x) satisfy (in terms of σ, b, and f ) in order that

be a martingale?