MathOverflow

Let the stopping time$$T_M = \inf \{ t \geq 0 : |R_{t} | \geq M \}.$$with $R_t$ given by the SDE:$$dR_t= ( R_t^2 - R_t)\,dt + |R_{t} |\,dWt. $$I would like to show that :$$\liminf_{M \to \infty} M\,\mathbb{P}\Bigl(T_M \leq t_0\Bigr) >0, $$for some...

In Jensen and Thomsen's Elements of KK-Theory, Lemma 2.1.18 gives a sufficient condition for two Kasparov $A$-$B$-bimodules $(E, \phi, F)$ and $(E, \phi, F')$ over separable C*-algebras $A$ and $B$ with the same underlying Hilbert $C*$-module structures...

A commutative ring with identity is called a chain ring if all its ideals form a chain under inclusion.
I want to know if there is a standard method to imbed a field $k$ in a chain ring of greater Krull dimensions? for example of Krull dimension 2?

On a measurable space $(E,\mathcal E)$, a stochastic kernel is a function $p\colon E\times \mathcal E\to [0,1]$ such that:
for each $x\in E$, the function $A\mapsto p(x,A)$ is a probability measure;
for each $A\in\mathcal E$, the function $x\mapsto p(x,A)$ is measurable....