We provide existence, uniqueness and stability results for affine stochastic Volterra equations with L1-kernels jumps. Such arise as scaling limits of branching processes in population genetics self-exciting Hawkes mathematical finance. The strategy we adopt the existence part is based on approximations using L2-kernels combined a general result. Most importantly, establish weak duality argumen...

Jointly controlled paths as used in Hairer and Gerasimovičs (2019), are a class of two-parameter $Y$ by $p$-rough path $X$ for $2 \leq p < 3$ each time variable, serve twice integrable with respect to $X$. We extend the notion jointly $\tilde{p}$-rough $\tilde{X}$ (on finite dimensional spaces) arbitrary $p$ $\tilde{p}$, develop corresponding integration theory this paths. In particular, we sho...

Cereal Chem. 75(1):129–136 Several varieties of rough rice that were either stored for an extended period of time or freshly harvested were conditioned to initial moisture contents ranging from 10 to 17%. After the individual kernel moisture content distributions were measured, the samples were soaked in water at temperatures ranging from 10 to 40°C. The samples were then dried and milled. The ...

*Correspondence: [email protected] Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan Abstract In this article, we establish Lp estimates for parametric Marcinkiewicz integral operators with rough kernels. These estimates and extrapolation arguments improve and extend some known results on Marcinkiewicz integrals. MSC: Primary 40B20; secondary 4...

Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L → L for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H1(Sn−1).

Convolution type Calderr on-Zygmund singular integral operators with rough kernels p.v. (x)=jxj n are studied. A condition on implying that the corresponding singular integrals and maximal singular integrals map L p ! L p for 1 < p < 1 is obtained. This condition is shown to be diierent from the condition 2 H 1 (S n?1).

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...