Ito and Stratonovich Solutions of the Linear Growth Model

    
Define Ito and Stratonovich processes with the same SDE :
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Find mean and variance functions for the Ito process:
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The mean and variance functions for the Stratonovich process are different:
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When , the Ito solution almost surely converges to zero, i.e. the large limit of probability that process value is does not exceed equals :
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Confirm it using simulations:
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When , the Stratonovich solution, however, almost surely diverges, i.e. the large limit of the probability that process value exceeds equals :
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Confirm it using simulations:
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