Small-time expansions for state-dependent local jump–diffusion models with infinite jump activity
نویسندگان
چکیده
منابع مشابه
Small-time expansions for local jump-diffusions models with infinite jump activity
We consider a Markov process {X t }t≥0 with initial condition X (x) t = x, which is the solution of a stochastic differential equation driven by a Lévy process Z and an independent Wiener process W . Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of Z, we obtain a small-time second-order po...
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We consider a Markov process X which is the solution of a stochastic differential equation driven by a Lévy process Z and an independent Wiener process W . Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Lévy density of Z outside any neighborhood of the origin, we obtain a small-time secondorder polynomi...
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15 صفحه اولJump locations of jump-diffusion processes with state-dependent rates
We propose a general framework for studying statistics of jump-diffusion systems driven by both Brownian noise (diffusion) and a jump process with state-dependent intensity. Of particular natural interest in many physical systems are the jump locations: the system evaluated at the jump times. As an example, this could be the voltage at which a neuron fires, or the so-called ‘threshold voltage’....
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2018
ISSN: 0304-4149
DOI: 10.1016/j.spa.2018.02.001