User obviousjoe - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T23:40:30Z http://mathoverflow.net/feeds/user/15544 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/66674/a-bjection-between-two-stochastic-processes/66757#66757 Answer by Obviousjoe for A bjection between two stochastic processes Obviousjoe 2011-06-02T17:49:06Z 2011-06-02T17:49:06Z <p>If f is continuous, differentiable and strictly increasing, the answer is yes. It is easy to see that y(t_n) is conditionally independent of y(t_1), y(t_2), y(t_{n-2}) given y(t_{n-1}), as this is the equivalent property enjoyed by x(t) when it is Markov. x(\tilde{t}_n}) is independent of x(\tilde{t}<em>1),...,x(\tilde{t}</em>{n-2}) conditional on x(\tilde{t}_{n-1}) as long as the \tilde{t}_k form a strictly increasing sequence. </p>