Stochastic differential equations driven by symmetric stable processes
By Richard F. Bass. 2003
58 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/24a534488c64756d233971e927fb93ee1d698f79
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Citations in the corpus
- Strong solutions for stochastic differential equations with jumps (2009, background): “2) is finite, Bass [2] constructed a continuous function x → φ(x) having continuity modulus x → ρ(x) for which the pathwise uniqueness for (1.”
- Stochastic equations of non-negative processes with jumps (2008, background): “(1.1) By a result of Bass (2003), if {z(t)} is a symmetric stable process of order 1 α 2 and if φ(·) is a bounded continuous function with modulus of continuity ρ(·) satisfying ∫ 0+ 1 ρ(x)α dx = ∞, (1.2) then (1.1) admits a strong solution and the solution is pathwise unique.”
- Systems of equations driven by stable processes (2006, result): “However if the matrix-valued function A(x) = (Aij(x)) is merely uniformly nondegenerate, bounded and continuous, pathwise uniqueness needs not to hold in general even in the case of dimension d = 1. The latter fact is the main result of [BBC], which combined with that of [Km2] and [ B4 ] gives sharp”
- Jump type stochastic differential equations with non-Lipschitz coefficients: Non-confluence, Feller and strong Feller properties, and exponential ergodicity (2017, background): “To name just a few, Bass (2003) presents a sharp condition for existence and pathwise uniqueness for a one-dimensional SDE with a symmetric stable driving noise; Fu and Li (2010) and Li and Mytnik (2011) provide sufficient conditions for existence and pathwise uniqueness for one-dimensional jump typ”
- Strong solutions of jump-type stochastic equations (2012, unknown): “, [1, 2, 3, 10, 11, 13, 15] and the references therein.”