# Tagged Questions

A stochastic process is a collection of random variables usually indexed by a totally ordered set.

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### Does a theory of stochastic differential algebras exist?

My question is motivated primarily by finance, where a non-technical student will learn how to approach SDEs using the symbolic manipulation of Itô calculus and the few basic rules of Brownian motion, ...
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### Why, and how badly, does the proof of “no percolation at the critical point in half-spaces” fail for full spaces?

The proof by Barsky et. al. that there is no percolation in half-spaces proceeds by a dynamic renormalization argument. The proof couples critical percolation in the half-space $\mathbb{H}^d$ with a ...
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### Do isonormal Gaussian processes have measurable sample paths?

Let $H$ be a real separable Hilbert space. Let $W=\{W(h):h\in H\}$ be a real-valued stochastic process defined on a complete probability space $(\Omega,\mathcal{F},P)$. Assume that $W$ is a centered ...
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### Doob's inequality for martingale “convolution”

Let $(X_t, t \in \mathbb{N})$ be a martingale, and let $a \leq b \leq T \in \mathbb{N}$ be constants. Is there something like Doob's inequality for $\mathbb{E} \sup_{a \leq t \leq b} X_t(X_T-X_t)$, i....
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### Feynman-Kac formula and time-ordering for vector bundles

Let $M$ be a compact Riemannian manifold and let $\mathrm{d}\mathbb{W}^{yx;T}(\gamma)$ denote the Brownian Bridge measure, i.e. the Wiener measure on the paths that travel from $x$ to $y$ in time $T$ (...
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### A question on improper Itô integrals and semimartingales

I am reading the article given in http://link.springer.com/chapter/10.1007/978-1-4614-5906-4_24#page-1. I have the following two questions: In which setting does one define improper integrals with ...
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I'm stuck on the trivial problem of showing memorylessness of holding (residence) times for a continuous time homogeneous Markov chain on finite state space. I have a homogeneous Markov process $x(t),... 0answers 102 views ### Solve SDE$dX_t=(c+\sigma_\zeta W'_tX_t)dt + \sigma_\epsilon dW_t$I am trying to solve the following SDE $$dX_t=(c+\sigma_\zeta W'_tX_t)dt + \sigma_\epsilon dW_t$$$c\in \mathbb{R}$is a constant,$X_t$is a stochastic process,$\sigma_\zeta,\sigma_\epsilon \in \...
Let $W$ be a $d$-dimensional Brownian motion and $X$ the strong solution to $$\mathrm{d} X = \mu(X)\mathrm{d} t + \sigma(X)\mathrm{d} W,$$ starting from some $x$, where $\mu$ and $\sigma$ are ...
Consider a uniform vector matroid $M(0)=U_{m,n}$ of rank $m$ with $n$ points, $n>m>2$ (you can think of it as a set of $n$ points in general position in vector space $F^m$ for some large field \$...