question archive 2) Solve the stochastic differential equation dx = −αt2x dt + g dW, and calculuate E[x(t)] and V [x(t)]
2) Solve the stochastic differential equation dx = −αt2x dt + g dW, and calculuate E[x(t)] and V [x(t)]
Subject:StatisticsPrice: Bought3
2) Solve the stochastic differential equation
dx = −αt2x dt + g dW,
and calculuate E[x(t)] and V [x(t)].
Hint: use the same method as for the Ornstein-Uhlenbeck equation. First solve the differential equation with g = 0, which will inform you of the appropriate transformation to a new variable, so that the new variable is constant when g = 0. The stochastic equation for the new variable will be easy to solve.
