applied stochastic processess
Ornstein-Uhlenbeck process is described by di⁄usion equation
∂P(z,t))/∂t = k*(∂P(z,t))/∂z + (B/2)*(∂^2P(z,t))/(∂z^2) -> eqn(1)
Assuming initial condition Z(0) = 0; seek its solution in the form
P(z; t) = 1/√(2πg(t)) exp^(-z^2/2g(t) )
Substitute this form into eq.1 and derive ODE for g(t): What is the appropriate initial condition?
Find its solution and write a nal solution for eq.1.
∂P(z,t))/∂t = k*(∂P(z,t))/∂z + (B/2)*(∂^2P(z,t))/(∂z^2) -> eqn(1)
Assuming initial condition Z(0) = 0; seek its solution in the form
P(z; t) = 1/√(2πg(t)) exp^(-z^2/2g(t) )
Substitute this form into eq.1 and derive ODE for g(t): What is the appropriate initial condition?
Find its solution and write a nal solution for eq.1.
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