Sorry if this is in the wrong section but i have a problem, I have no experience with stochastic equations well analytically anyway. The equation i have is the following; [itex]\frac{dv}{dt} = - \alpha v+ \lambda F+\eta[/itex] Where alpha lambda and F are constants, v is a variable (speed in this case) and eta is a random value. I believe this is similar to Brownian motion with an applied field, although i have no idea how to solve this analytically i plan to solve it analytically and compare it to a numerical solution. So any help will be most appreciated!
This will turn into a standard equation of the type dv/dt=kv+ noise after a change of variable. For some general methods for solving SDEs, I hope the following link will be of much help - http://math.berkeley.edu/~evans/SDE.course.pdf