Symmetric Stable Laws and Stable‐Like Jump‐Diffusions

By Vassili N. Kolokoltsov. 2000

209 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d23993724806d6b61ddc86fff57e399a703c6639

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Citations in the corpus

Transition Probabilities for Symmetric Jump Processes (2002, methodology): “Previous work related to this paper includes [ Kl ] and [Km].”
Weighted Poincaré inequality and heat kernel estimates for finite range jump processes (2008, background): “In [27], Kolokoltsov obtained two-sided heat kernel estimates for certain stable-like processes in Rd , whose infinitesimal generators are a class of pseudodifferential operators having smooth symbols.”
Heat kernels for non-symmetric diffusion operators with jumps (2016, methodology): “For example, Kolokoltsov [22] obtained two-sided heat kernel estimatesfor certain stable-like processes in R d, whose infinitesimal generators are a class of pseudo-differential operators having smooth symbols.”
Levy-Type Processes and Pseudodifferential Operators (2001, methodology): “(3) Find a fundamental solution for the operator /; + q(x, D) by a parametrix method and prove that this fundamental solution gives rise to a transition function, see [23], [78], or [88], as well as [77].”
Transition Density Estimates for a Class of Lévy and Lévy-Type Processes (2009, methodology): “Two-sided heat kernel estimates for a class of stable-like processes in Rn were obtained by Kolokoltsov [29]; Bass and Levin [4] used a completely different approach to get transition density estimates for discrete time Markov chains in Zd with certain conductance.”
A Widder’s Type Theorem for the Heat Equation with Nonlocal Diffusion (2013, background): “By [9] (see also [2] and [4]) we know that (2.”
Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise (2014, methodology): “Therefore we do not use the above argument from [37] for the derivative ∂x , and develop another way to justify the whole method.”
Heat kernel estimates for jump processes of mixed types on metric measure spaces (2007, methodology): “In [18], Kolokoltsov obtained two-sided heat kernel estimate for certain stable-like processes in Rd.”
Symmetric jump processes and their heat kernel estimates (2009, background): “In [29], Kolokoltsov obtained two-sided heat kernel estimates for certain stable-like processes in Rn, whose infinitesimal generators are a class of pseudo-differential operators having smooth symbols.”
The Influence of Fractional Diffusion in Fisher-KPP Equations (2012, unknown): “8) is satisfied; see for instance [14].”
Harnack inequality for some classes of Markov processes (2004, methodology): “In [7] Kolokoltsov proved detailed estimates on the transition density of symmetric α-stable processes whose Lévy measures are comparable to the Lévy measure of the rotationally invariant α-stable process.”