8 problems

Let $X_t$ be the limiting measure-valued process characterized above, and let $d$ denote the spatial dimension. A Girsanov theorem relates the law of $X_t$ to that of a standard su…

Applicability conjecture. The above techniques could be applied in this setting of interacting populations with fluctuating population size.

The paper considers Theorems 1 and 2 concerning the existence and characterization of a self-similar measure-valued process and its associated Lamperti transformation. Generalizati…

Let $d\leq 3$, set $\gamma=\frac{2d}{6-d}$, and suppose that for an appropriate family of initial measures $X_0^R$ one has $X_0^R\Rightarrow X_0$, where $X_0$ is a fixed compactly…

Density conjecture. A density for $X_t$ exists only when $d=1$.

Let $X_\infty$ be the Kingman measure tree, and for $\lambda>0$ define the process $\mathcal Z^\lambda=(Z_t^\lambda)_{t\geq 0}$ by … Suppose that $\lambda_n\to\infty$ and that, alo…

Let $X$ be a measure-valued process governed by the martingale problem for the measure-valued SIR epidemic process, and let $\theta$ denote its transmission rate. The process survi…

Convergence conjecture. The deterministic measure-valued process $v_t$ converges for large time $t$ towards the following stationary value.