In the core reading it states that a process with independent increments has the markov property. However, independent increments is independent of the current time t. From my understanding, this contradicts the markov property that states future probabilities depend only on the current state at t?
Hi I think you may have confused the increments with the value of the process here. Consider a simple random walk defined on the integers with equally probable increments of +/-1. The increments here are clearly independent of time t and previous increments, hence this process has the Markov property. However the next value of the process depends on the current value even though the increments do not depend on t, since the next value must be Xt + 1 or Xt - 1. Hopefully that clears things up. Dave
