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# All Questions

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### Floquet stochastic process

Let $X_t$ be defined by the SDE $$dX_t = A(t, X_t)dt + dW_t$$ where $A(t, X_t)$ is linear in $X_t$ and periodic in $t$. Assume also that the process is stable. If $A(\cdot)$ didn't have $t$ ...
178 views

### Is there a Feynman-Kac formula for vector-valued Schrödinger operators?

Given a vector function $$f=(f_1,\ldots,f_n)\in L^2(\mathbb R,\mathbb R^n)$$ (for some $n\in\mathbb N$), let us define $$\Delta f:=(\Delta f_1,\ldots,\Delta f_n),$$ where $\Delta$ is the Laplacian ...
118 views

### Stochastic Approximation in Reproducing Kernel Hilbert Space

Consider an iterative algorithm with incremental updates \begin{align} x_{t+1} = x_t + \alpha_t \cdot [ h(x_t) + M_{t+1}], \end{align} where $\{x_t \}_{t \geq 0}$ is in a reproducing kernel Hilbert ...
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238 views

### Lorenz attractor power spectrum

If considered Lorenz attractor (with classical parameters $\sigma = 10, b = \frac{8}{3},r>25$), it is often noted, that while the spectral density (Fourier transformation of corresponding ...
571 views

### Branching Brownian Motion and the KPP equation

I have troubles understanding the proof of the connection between BBM and KPP equation. I mean the proof of the next lemma from the lecture notes of Anton Bovier about BBM, link. This is almost whole ...
2k views

### Any suggestions on a rigorous stochastic differential equations book?

I have been looking through some books and they are not very rigorous. Any suggestions would be great.

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