Abstract
For a certain kind of nonlinear stochastic differential equations with jumps in ℝd, there exists an invariant probability measure µ on ℝd. A Lyapunov exponent q µ can be represented by the Furstenberg—Has’minskii formula as an integral over ℝd with respect to the ergodic invariant measure, so that the almost sure asymptotic stability depends on the sign of q µ . If the corresponding diffusion is nondegenerate, then µ is unique and has strictly positive invariant density in C(ℝd).
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Li, C.W. (2003). Lyapunov Exponents of Nonlinear Stochastic Differential Equations with Jumps. In: Giné, E., Houdré, C., Nualart, D. (eds) Stochastic Inequalities and Applications. Progress in Probability, vol 56. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8069-5_19
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DOI: https://doi.org/10.1007/978-3-0348-8069-5_19
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