The martingale problem for a class of nonlocal operators of diagonal type

Chaker, Jamil

doi:10.1002/mana.201800452

Cited by 13 publications

(5 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, Y d ) under certain assumptions on the matrix A. For the case where Z i 's are independent α i -stable processes with different α i , a similar result was obtained in [8] (see [7] for the uniqueness of weak solutions for diagonal matrix A). In [9], the authors investigated Poisson equations with singular anisotropic operators such as A in (1.1).…”

Section: ˆR3supporting

confidence: 53%

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Ho¹

2023

Preprint

View full text Add to dashboard Cite

Since the Seoul Metropolitan Area, Republic of Korea, is highly populated, a large number of people are frequently exposed to high concentrations of particulate matter (PM) with mean aerodynamic diameters of <= 10 mm (PM10) in cold season. The concentration of PM10 in Seoul Metropolitan Area increases by transboundary transport, local direct emissions, and chemical reactions of aerosol precursors in the atmosphere. Here, the Seoul Metropolitan Area (Seoul, Gyeonggi-do, and Incheon) and surrounding region (Chungcheongnam-do, Daejeon, and Sejong) are regionally classified by clustering analysis based on the variability of PM10 concentrations. According to the inertia score by the number of clusters, the optimum cluster number of regional variability of PM10 is four. The region of cluster 1 is divided into southern Gyeonggi-do and eastern Chungcheongnam-do, the cluster 2 is mainly classified Incheon, western Gyeonggi-do, and Seoul. The cluster 3 region is western Chungcheongnam-do adjacent to Yellow Sea, and the cluster 4 is classified into eastern Gyeonggi-do. The variability of PM10 in each region is distinguished by the local chemical pollutants emission and weather conditions such as wind speed and direction in each region. This regional classification of PM10 variability is different from administrative districts. Considering most of policies for responding to high concentrations of PM10 are being prepared by administrative districts, this study suggests that a response on the basis of these regional PM10 distribution would be more effective way to improve air quality in the Seoul Metropolitan and Chungcheong Area.

show abstract

Section: ˆR3supporting

confidence: 53%

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Ho¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In recent years singular, nonlocal Lévy operators have been intensively studied both by probabilists and specialists in PDEs, see e.g. [4,5,7,8,10,22,23,24,28]. An interesting open problem is the following.…”

Section: Introductionmentioning

confidence: 99%

Strong Feller Property for SDEs Driven by Multiplicative Cylindrical Stable Noise

2020

View full text Add to dashboard Cite

We consider the stochastic differential equation dX t = A(X t−) dZ t , X 0 = x, driven by cylindrical α-stable process Z t in , where α ∈ (0, 1) and d ≥ 2. We assume that the determinant of A(x) = (a ij (x)) is bounded away from zero, and a ij (x) are bounded and Lipschitz continuous. We show that for any fixed γ ∈ (0, α) the semigroup P t of the process X t satisfies |P t f (x)−P t f (y)| ≤ ct −γ /α |x−y| γ ||f || ∞ for arbitrary bounded Borel function f. Our approach is based on Levi's method.

show abstract

“…In this case, the results of [DF13] are extended in [FJR18]. Uniqueness and existence of weak solutions is proved in [Cha19] under the additional assumption that the matrix A ik is diagonal.…”

Section: Theorem 15 (Hölder Regularity Estimate)mentioning

confidence: 99%

Robust Hölder Estimates for Parabolic Nonlocal Operators

Chaker¹,

Kaßmann²,

Marvin³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

In this work we study parabolic equations determined by nonlocal operators in a general framework of bounded and measurable coefficients. Our emphasis is on the weak Harnack inequality and Hölder regularity estimates for solutions of such equations. We allow the underlying jump measures to be singular with a singularity that depends on the coordinate direction. This approach also allows to study several classes of non-singular jump measures that have not been dealt with so far. The main estimates are robust in the sense that the constants can be chosen independently of the order of differentiability of the operators.

show abstract

The martingale problem for a class of nonlocal operators of diagonal type

Cited by 13 publications

References 23 publications

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Regional classification according to PM10 concentrations in the Seoul Metropolitan and Chungcheong Area, Republic of Korea

Strong Feller Property for SDEs Driven by Multiplicative Cylindrical Stable Noise

Robust Hölder Estimates for Parabolic Nonlocal Operators

Contact Info

Product

Resources

About