Weak Euler Scheme for Lévy-Driven Stochastic Differential Equations
R. Mikulevicius,Changyong Zhang +1 more
TLDR
In this article, the authors studied the convergence rate of the weak Euler approximation for solutions to Levy-driven stochastic differential equations with non-egenerate main part driven by a spherically symmetrized sparsification.Abstract:
This paper studies the rate of convergence of the weak Euler approximation for solutions to Levy-driven stochastic differential equations with nondegenerate main part driven by a spherically symmet...read more
Citations
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Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Book
Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Journal ArticleDOI
Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation
TL;DR: Weak convergence of the considered algorithm is proved and an in-depth analysis of how its error and computational cost depend on the jump activity level is presented.
Journal ArticleDOI
Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation
TL;DR: In this article, the authors considered stochastic differential equations driven by a general Levy processes with infinite activity and the related Dirichlet problem for parabolic integro-differential equation (PIDE).
References
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Book
Interpolation Spaces: An Introduction
Jöran Bergh,Jörgen Löfström +1 more
TL;DR: In this paper, the authors define the Riesz-Thorin Theorem as a necessary and sufficient condition for interpolation spaces, and apply it to approximate spaces in the context of vector spaces.
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Lévy Processes and Stochastic Calculus
TL;DR: In this paper, the authors present a general theory of Levy processes and a stochastic calculus for Levy processes in a direct and accessible way, including necessary and sufficient conditions for Levy process to have finite moments.
Book ChapterDOI
Stochastic Differential Equations
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Book
Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Book
Fully Nonlinear Elliptic Equations
Luis A. Caffarelli,Xavier Cabré +1 more
TL;DR: The Dirichlet problem for concave equations has been studied in this article, where Alexandroff estimate and maximum principle Harnack inequality uniqueness of solutions Concave equations $W^{2,p}$ regularity Holder regularity
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