Errata for Stochastic calculus for symmetric Markov processes
نویسندگان
چکیده
منابع مشابه
Stochastic Calculus for Symmetric Markov Processes
Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained. AMS 2000 Mathematics Subject Classification: Primary 31C25; Secondary 60J57, 60J55, 60H05.
متن کاملMarkov Processes and Stochastic Calculus
• Ω: An abstract space of points ω ∈ Ω. • F : a σ-field (or σ-algebra) on Ω. That is, a collection of subsets of Ω satisfying: 1. Ω ∈ F . 2. Let A ⊆ Ω such that A ∈ F then Ac = Ω−A ∈ F . 3. Let A1, A2, A3, · · · ∈ F then A1 ∪A2 ∪A3 ∪ · · · ∈ F . The elements of F are called events. Condition (1) above simply states that the space Ω is necessarily an event. Conditions (2) and (3) state that the ...
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For these harmonic functions we investigate a certain boundary value problem which is analogous to the Dirichlet problem associated with a single process. One basic tool for this study is a generalization of Dynkin's formula, which can be thought of as a kind of stochastic Green's formula. Another important tool is the use of Markov processes~, obtained from x;, by certain random time changes. ...
متن کاملStochastic Calculus for Dirichlet Processes
Using time-reversal, we introduce the stochastic integration for zero-energy additive functionals of symmetric Markov processes, which extends an early work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained. AMS 2000 Mathematics Subject Classification: Primary 31C25; Secondary 60J57, 60J55, 60H05.
متن کاملMarkov chain approximations for symmetric jump processes
Markov chain approximations of symmetric jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a symmetric jump process with state space Rd the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space Hα/2(Rd), α ∈ (0, 2), that is equivalent to the standard one.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2012
ISSN: 0091-1798
DOI: 10.1214/11-aop684