Stochastic population dynamics driven by Lévy noise

• DOI: 10.1016/j.jmaa.2012.02.043
• Publication Date: 2012-02-28T18:01:57Z
• Authors: Jianhai Bao; Chenggui Yuan
• Keywords: Pathwise estimation; Applied Mathematics; Probability (math.PR); 01 natural sciences; Lévy noise; 93D05, 60J60, 60J05; Exponential martingale inequality with jumps; FOS: Mathematics; Brownian motion; 0101 mathematics; Analysis; Mathematics - Probability

This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a unique global positive solution; (b) Applying an exponential martingale inequality with jumps, we discuss the asymptotic pathwise estimation of such model.<br/>16 pages<br/>