Wiener process probability

Calculate with what probability it will happen that the random trajectory of the Wiener process will acquire a value greater than 2 at time 2 and a value less than 2 at time 3.

Answer

Answers can be viewed only if
  1. The questioner was satisfied and accepted the answer, or
  2. The answer was disputed, but the judge evaluated it as 100% correct.
View the answer
  • Hello, thank you for your answer! Could you please tell me how did you calculate the double integral? Thank you for your response.

  • @Green: Please respond to Kingroma99 question above.

  • @Kingroma99, the double integral was evaluated numerically. Otherwise one can compute it by first treating t as a constant, and integrating from negative infinity to 2-s. This involves the error function, which is the antiderivative of the Gaussian. Then, the result can be integrated with respect to t from 2 to infinity. To get a closed form in terms of error functions, one follows the above procedure while doing a few integral substitutions.

The answer is accepted.