2
votes
2answers
67 views

The answer of the following stochastic differential equation

I want to solve the following stochastic differential equation $$dX_t=(a(t)+b(t)X_t)dt+(c(t)+d(t)X_t)dB_t$$ where $a,b,c,d$ are continious functions and we have the initial condition $X_0=x$ .
1
vote
0answers
228 views

Show that this is the unique solution of that Stochastic Differential Equation

Reading through a paper, I stumbled across the stochastic differential equation $ dS_t = \sigma S_{t-} dX_t $. The claim there was that $ S_t = S_0 \exp(\alpha N_t - \beta t) $ should be its unique ...