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Register a new userProperties of Switching Jump Diffusions: Maximum Principles and Harnack Inequalities
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This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated operators for switching jump diffusions are non-local, resulting in more difficulty in treating such systems. Our study is carried out by taking into consideration of the interplay of stochastic processes and the associated systems of integro-differential equations.
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This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further helps to derive easily verifiable conditions for linear systems. For one-dimensional linear regime-switching jump diffusions, necessary and sufficient conditions for almost sure and $p$th moment exponential stabilities are presented. Several examples are provided for illustration.
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying processes feature in the switching process depends on the jump diffusions. In this paper, conditions for recurrence and positive recurrence are derived. Ergodicity is examined in detail. Existence of invariant probability measures is proved.
We prove sharp Harnack inequalities for a family of Kolmogorov-Fokker-Planck type hypoelliptic diffusions.
The Harnack and log Harnack inequalities for stochastic differential equation driven by $G$-Brownian motion with multiplicative noise are derived by means of coupling by change of mesure. All of the above results extend the existing ones in the linear expectation setting. Moreover, the gradient estimate generalize the nonlinear results appeared in [11].
In this paper we use splitting technique to estimate the probability of hitting a rare but critical set by the continuous component of a switching diffusion. Instead of following classical approach we use Wonham filter to achieve multiple goals including reduction of asymptotic variance and exemption from sampling the discrete components.
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