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Observing that the recent developments of the recursive (product) quantization method induces a family of Markov chains which includes all standard discretization schemes of diffusions processes , we propose to compute a general error bound induced by the recursive quantization schemes using this generic markovian structure. Furthermore, we compute a marginal weak error for the recursive quantization. We also extend the recursive quantization method to the Euler scheme associated to diffusion processes with jumps, which still have this markovian structure, and we say how to compute the recursive quantization and the associated weights and transition weights.
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 fea
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
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 deriv
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and payoff functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics f
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach consists in poi