A study of a class of stochastic differential equations with non-Lipschitzian coefficients

By S. Fang, Tusheng Zhang. 2005

154 citations recorded by the source corpus.

Subfields: Applied Mathematics, Demography, Finance

View Paper: https://www.semanticscholar.org/paper/eace0bce9541ba969ffd34e5bafc89eba8062802

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Tusheng Zhang
2. Xicheng Zhang
3. Chao Zhu
4. Fubao Xi
5. Davar Khoshnevisan
6. Robert C. Dalang
7. Zenghu Li
8. Donald A. Dawson

In Demography

1. Xicheng Zhang
2. Davar Khoshnevisan
3. Chao Zhu
4. Fubao Xi
5. Robert C. Dalang
6. Zenghu Li
7. Donald A. Dawson
8. Xue-peng Bai

In Finance

1. Tusheng Zhang
2. Chao Zhu
3. Robert C. Dalang
4. Zenghu Li
5. Fubao Xi
6. Xicheng Zhang
7. Davar Khoshnevisan
8. Donald A. Dawson

Citations in the corpus

• Flow of diffeomorphisms for SDEs with unbounded H (2009, unknown): “36 68 v1 [ m at h. PR”
• Stochastic flows of SDEs with irregular coefficients and stochastic transport equations (2009, background): “Recently, there are increasing interests for studying the stochastic homeomorphism flow property associated with SDE (1.1) under variousnon-Lipschitz assumptions onb andσ (cf. [21, 1, 20, 25, 8, 9, 10, 11, 28], etc.).”
• Jump type stochastic differential equations with non-Lipschitz coefficients: Non-confluence, Feller and strong Feller properties, and exponential ergodicity (2017, methodology): “12) do not satisfy conditions (H1) and (H2) in Fang and Zhang (2005) since σ and b grow very fast in the neighborhood of ∞ and they are Hölder continuous with orders 2 3 and 1 3 , respectively.”
• Skew convolution semigroups and affine Markov processes (2005, result): “The result may be regarded as an extension of the well-known result of Yamada and Watanabe [29]; see also [13] and the references therein for various generalizations of their result in the setting of diffusion processes.”
• Local and global well-posedness of SPDE with generalized coercivity conditions☆ (2012, unknown): “[18]).”
• Global solutions to stochastic reaction–diffusion equations with super-linear drift and multiplicative noise (2019, methodology): “Theorem 1.4 is an infinite-dimensional variation on aspects of the theory of Fang and Zhang [12] on stochastic differential equations with superlinear coefficients.”
• On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients (2010, background): “Remark: Fang and Zhang prove in [12] a similar uniqueness result for stochastic differential equations, where ρ need not to be concave by a stopping time technique.”