Thinning and multilevel Monte Carlo methods for piecewise deterministic (Markov) processes with an application to a stochastic Morris–Lecar model
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DOI: 10.1017/apr.2019.55
Abstract: Abstract In the first part of this paper we study approximations of trajectories of piecewise deterministic processes (PDPs) when the flow is not given explicitly by the thinning method. We also establish a strong error… read more here.
Keywords: multilevel monte; monte carlo; markov processes; piecewise deterministic ... See more keywords
Approximation methods for piecewise deterministic Markov processes and their costs
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DOI: 10.1080/03461238.2018.1560357
Abstract: ABSTRACT In this paper, we analyse piecewise deterministic Markov processes (PDMPs), as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of PDMPs. There one is… read more here.
Keywords: approximation; monte carlo; piecewise deterministic; deterministic markov ... See more keywords
Supports of invariant measures for piecewise deterministic Markov processes
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DOI: 10.1088/1361-6544/aa7e94
Abstract: For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant control sets… read more here.
Keywords: supports invariant; piecewise deterministic; deterministic markov; markov processes ... See more keywords
Numerical methods for piecewise deterministic Markov processes with boundary
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DOI: 10.1093/imanum/drv069
Abstract: We study the approximation of the distribution of Piecewise Deterministic Markov Processes jumping when the process reaches some boundary of the domain. We first introduce an equation to which the marginal distributions of the process… read more here.
Keywords: piecewise deterministic; numerical methods; marginal distributions; deterministic markov ... See more keywords