All Questions

I am broadly working on a dynamic process where we want to see how a field $\rho(r)$ changes in space in time with thermal noise. The system is biased around a thermodynamic saddle point dictated by $...

Setup Let $X_t$ be a $d$-dimensional diffusion process solving the Ito-stochastic differential equation $$ X_t = x+ \int_0^t f(X_t,u_t)dt + \int_0^t \sigma dW_t, $$ where $x \in \mathbb{R}^d$, $u_t$ ...

Are there any example of SDEs with constant diffusion terms, other than the Ornstein Uhlenbeck process, which have exact solutions? I'm thinking of something of the form: \begin{equation} dX_t = f(...

Suppose we have a time-series $x(t_i)$ at discrete times $t_i$ and we want to estimate the parameters of an underlying SDE corresponding to this time-series: $$dx_t = f(x_t,\theta)dt + \sigma(x_t,\...