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            <title xml:lang="en">A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems (extended version)</title>
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            <idno type="halRefHtml">&lt;i&gt;Nonlinear Analysis: Hybrid Systems&lt;/i&gt;, 2010, 4 (2), pp.357-370. &lt;a target="_blank" href="https://dx.doi.org/10.1016/j.nahs.2009.07.008"&gt;&amp;#x27E8;10.1016/j.nahs.2009.07.008&amp;#x27E9;&lt;/a&gt;</idno>
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            <note type="commentary">This paper is an extended version of my IFAC WC'2008 paper with the same name (preprint available as arXiv:0801.3725v2 and hal-00215938). It is published in a special issue of "Nonlinear Analysis: Hybrid Systems" (Elsevier) related to the 2008 IFAC World Congress.</note>
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                <term xml:lang="en">Fokker-Planck equation</term>
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                <term xml:lang="en">Stochastic system with jumps</term>
                <term xml:lang="en">Markov processes</term>
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              <p>A general formulation of the Fokker-Planck-Kolmogorov (FPK) equation for stochastic hybrid systems is presented, within the framework of Generalized Stochastic Hybrid Systems (GSHSs). The FPK equation describes the time evolution of the probability law of the hybrid state. Our derivation is based on the concept of mean jump intensity, which is related to both the usual stochastic intensity (in the case of spontaneous jumps) and the notion of probability current (in the case of forced jumps). This work unifies all previously known instances of the FPK equation for stochastic hybrid systems, and provides GSHS practitioners with a tool to derive the correct evolution equation for the probability law of the state in any given example.</p>
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