Stochastic Differential Equation for Exponential Decay

    
Define a stochastic process satisfying Ito stochastic differential equation , describing exponential decay subject to Wiener noise:
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Simulate the process for different values of variance parameter :
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Find the mean function of the process:
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Its independence of the noise variance suggests that it coincides with the deterministic solution:
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Find the variance function of the process :
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Value of the process at time is a random variable. Find the probability density function of the value of the process :
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