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.


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  • 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.

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