| Probability theory originated in the middle of the 17th century,it is one of the mainstream branches of modern mathematical theory.With the continuous progress of modern natural science,probability theory has been widely applied to all aspects of production and life,and it has achieved certain results.By using probability theory,stochastic analysis and stochastic dynamic system theory,we study the dynamic properties of financial chaotic systems driven Lévy process.The research contents are as follows:In Chapter 1,We mainly introduce the background,significance and some preliminary knowledge,and we also introduce the main content and framework.In Chapter 2,We mainly study attractors and bifurcations of stochastic fi-nancial chaotic systems.By ingeniously constructing Lyapunov function,using the probability measure,Hessian matrix,least squares method and stochastic dy-namic system,we study the global exponential attraction set,ultimately bound-ed,random attractor and bifurcation phenomena of stochastic financial chaotic system solutions.In Chapter 3,we mainly study the asymptotic stability of financial chaotic system driven by Lévy process.By using martingale theory,Jensen inequality and measure function,we prove the existence of global positive solutions and invariant probability measures for stochastic financial chaotic systems,and we further studied the asymptotic stability of stochastic financial chaotic systems.In Chapter 4,we mainly study the random periodic solutions of a stochas-tic financial chaotic system driven by Lévy process.By using the properties of periodic Markov processes,non-Gauss properties,exponential martingale inequal-ities,we prove the existence uniqueness and pth asymptotic stability of solutions for stochastic financial chaotic systems.Furthermore,we obtain the existence and uniqueness conditions of random periodic solutions for stochastic financial chaotic systems. |
