# Questions tagged [stochastic-differential-equations]

Stochastic ordinary and partial differential equations generalize the concepts of ordinary and partial differential equations to the setting where the unknown is a stochastic process.

514 questions
Filter by
Sorted by
Tagged with
68 views

### Fokker-Planck equation for SDEs on manifold

Let $M_d$ be the set of $d\times d$ complex matrices and $S_d\subset M_d$ be its subset of density matrices, i.e. $A\in S_d$ iff $A\ge 0$, $A^*=A$ and $tr(A)=1$, where $A^*$ denotes the conjugate ...
82 views

### Strong blow up limits for SDE

Note: This is a strengthening of the following result, motivated by the need for strong convergence in applications. Let $W$ be a one dimensional standard Brownian motion, and let $X$ be the solution ...
1 vote
73 views

68 views

21 views

### Langevin dynamics or stochastic gradient flow for grand canonical ensemble

We know that for a measure exp(-U(X)) (canonical ensemble), we can use the dynamic dX=-DU(X)+ noise to sample the measure as t goes to infinity. Is there any dynamic corresponding to the grand ...
153 views

### When does a solution to SDE have full support?

Suppose an $n$-dimensional process $(X_t)_{0 \leq t \leq 1}$ satisfies an SDE of the form: $$dX_t = u_t(X_t) \,dt + dB_t, ~~X_0 = 0$$ where $(B_t)_{t\geq 0}$ is a Brownian motion with $B_1 \sim N(0,K)$...
47 views

### Stochastic differential equations driven by composed Poisson process

Consider the stochastic differential equation as follows: $$X_t = x + \int_0^t b(X_s)\,ds + \int_0^t a(X_{s-})\,dL_s,\quad \forall t\ge 0,$$ where $L=(L_t)_{t\ge 0}$ denotes some Lévy process. What ...
208 views

107 views

### KL Divergence between the solution to two SDEs

What is the KL divergence between the laws of solutions to SDEs? That is, let \begin{align*} dX^1&=b_1(X^1,t) \, dt+\sigma(X^1,t) \, dB\\ dX^2&=b_2(X^2,t) \, dt+\sigma(X^2,t) \, dB \end{align*}...
1 vote
73 views

1 vote
47 views

347 views

### Riemannian metric induced by a stochastic differential equation

Following this paper, a diffusion process in $\mathcal{R}^d$ $$dX_t = f(X_t) \, dt + \sigma(X_t) \, dW_t ,$$ with $\sigma(x) \in \mathbb{R}^{d \times m}$ and $m$ dimensional Brownian motion can be ...
1 vote
166 views

### Is there an inverse Lamperti transformation for diffusions?

The Lamperti transformation is commonly used to transform SDEs with state dependent coefficients into SDEs with constant diffusion. For multidimensional processes there are some conditions on the ...
149 views

### Comparing diffusion processes in different metrics

I would like to know if it is possible to compare two diffusion processes defined on the same manifold $\mathcal{M}$ but with respect to different metrics say $g_1$ and $g_2$. Is there a way to apply ...
1 vote