Equivalence of Stochastic Equations and Martingale Problems
By Thomas G. Kurtz. 2011
138 citations recorded by the source corpus.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/50ea0ebc39c875be27c553bbd5827e43ebf5f580
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
- Chao Zhu
- Zenghu Li
- Fubao Xi
- Longmin Wang
- Niels Richard Hansen
- Alexander Sokol
- Donald A. Dawson
- Zhen-Qing Chen
In Mathematical Physics
- Zenghu Li
- Longmin Wang
- Chao Zhu
- Fubao Xi
- Donald A. Dawson
- Niels Richard Hansen
- Alexander Sokol
- Zhen-Qing Chen
Citations in the corpus
- Causal interpretation of stochastic differential equations (2013, background): “ satisfies (5.2) and X and X˜ has the same distribution. Now note that A0 is of the type given as (13) in [23]. As C is positive semidefinite, we have C = LLt for some L ∈ M(d,d). The condition (14) in [23] then in our case translates into having sup x∈K ka(x)αk2 +ka(x)Lk2 2 + Z D ka(x)uk2 2 dν(u) + Z”
- Stochastic equations, flows and measure-valued processes (2010, background): “See El Karoui and Méléard (1990) and Kurtz (2007, 2010) for the general theory of stochastic equations driven by white noises and Poisson random measures.”
- Jump type stochastic differential equations with non-Lipschitz coefficients: Non-confluence, Feller and strong Feller properties, and exponential ergodicity (2017, background): “We give a constructive proof motivated by Kurtz (2011).”
- Continuous Time Markov Chain Models for Chemical Reaction Networks (2011, unknown): “See [38] for a more detailed discussion.”
- Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow (2022, unknown): “Hence, the equivalence of Law( Z t ) and Law( X t ) follows if the solution of (11) is unique, which is equivalent to the uniqueness of the solution of d Z t = v X ( Z t , t ) following Corollary 1.3 of Kurtz [37] (see also Theorem 4.1 of Ambrosio and Crippa [1]).”
- Uniqueness of stable processes with drift (2013, methodology): “3) from the existence of the martingale problem for (Lb, C∞ c (Rd)) by applying results from [8] because Lbf is typically unbounded for f ∈ C∞ c (Rd).”