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We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regular...
Regularity properties such as the incoherence condition, the restricted isometry property, compatibility, restricted eigenvalue and $\ell_q$ sensitivity of covariate matrices play a pivotal role in hi...
We give a new proof of Makagon's and Weron's criterion for Jo-regularity (see [4], Theorem 5.3), and discuss some conditions of Jo-singularity of q-variate stationary processes.
In the paper we prove that the n-th directional derivative of a pstable density f (x) in the direction a can be estimated by where 0 < u < 1, and C depends also on geometrical properties of the Lkv...
Let X = (X,,Z E TN = [0, 1IN)b e a symmetric a-stable process, 1 < a < 2. Based on a Kolmogorov type continuity theorem we show Holder conditions in I?-norms for the local time of X with respect to...
We extend to the vector-valued situation some earlier work of Ciesielski and Roynette on the Besov regularity of the paths of the classical Brownian motion.We also consider a Brownian motion as a Be...
Existence and Regularity of Solutions to a Stochastic Burgers-Type Equation。
We prove the law of large numbers for U-statistics whose underlying sequence of random variables satisfies an absolute regularity condition ($beta$-mixing condition) under suboptimal conditions.

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