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Results tagged with ds.dynamical-systems
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user 46900
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
3
votes
0
answers
113
views
Stationarity of Brownian motion with drift
Suppose the following SDE for $X_t$ is well-posed:
$$dX_t = \sqrt{2}\, dB_t - \nabla\Phi(X_t)\,dt.$$
For what $\Phi\in C^1(R^d)$ will $X$ have stationary distribution $u_{\infty}$? For what $\Phi$ w …
- 165
1
vote
0
answers
72
views
Convergence to equilibrium for time in-homogeneous diffusions
Consider the long time behavior for a time in-homogeneous diffusion such as
$$dX_t = dB_t - \nabla V(X_t)\,dt + b_t(X_t)dt,$$
where $V(x)$ is a smooth convex function and $b_t(x)$ is a time-dependent …
- 165