Gradient estimate for Ornstein–Uhlenbeck jump processes

By Feng-Yu Wang. 2010

49 citations recorded by the source corpus.

By using absolutely continuous lower bounds of the Levy measure, explicit gradient estimates are derived for the semigroup of the corresponding Levy process with a linear drift. A derivative formula is presented for the conditional distribution of the process at time t under the condition that the process jumps before t. Finally, by using bounded perturbations of the Levy measure, the resulting gradient estimates are extended to linear SDEs driven by Levy-type processes.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21633aa57af810386f9e8d599f4ffa4eb77638d9

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Citations in the corpus

Harnack inequalities for stochastic equations driven by Levy noise (2012, background): “1(2) generalizes the main results in [16, 3, 12] for Lévy processes or linear equations driven by Lévy noise.”
Exponential ergodicity and regularity for equations with Lévy noise (2011, background): “Some related estimates were obtained in a recent paper [39] which however does not cover the present situation.”
Gradient estimates for SDEs driven by multiplicative Lévy noise (2013, methodology): “When bt(x) = Ax for a matrix A and σt(x) = Id, the gradient estimate of type |∇Ptf | 6 ‖f‖∞φ(t), t > 0, f ∈ Bb(R) has been derived in [13] by using lower bound conditions of the Lévy measure, and in [10] for A = 0 by using asymptotic behaviours of the symbol of Lt; see also [15] for a derivative for”