Vasicek model with mixed-exponential jumps and its applications in finance and insurance
Advances in Difference Equations, 2018 In this paper, the authors study the distribution of the Vasicek model with mixed-exponential jumps and its applications in finance and insurance. With the aid of the piecewise deterministic Markov process theory and the martingale theory, the authors ...
Yongfeng Wu, Xue Liang
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Polynomial Convergence Rates of Piecewise Deterministic Markov Processes
Methodology and Computing in Applied Probability, 2022 Abstract We consider piecewise-deterministic Markov processes such as the Bouncy Particle sampler, on target densities with polynomial tails. Using direct drift condition methods, we provide bounds on the polynomial order of the processes' convergence rate to stationary, on both one-dimensional and high-dimensional state spaces, in both total ...
Roberts, Gareth O. +1 more
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Numerical methods for piecewise deterministic Markov processes with boundary
ESAIM: Proceedings and Surveys, 2014 In this paper is described the general aspect of a numerical method for piecewise deterministic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov ...
Goudenège Ludovic
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Averaging for a Fully Coupled Piecewise-Deterministic Markov Process in Infinite Dimensions [PDF]
Advances in Applied Probability, 2011 In this paper we consider the generalized Hodgkin-Huxley model introduced in Austin (2008). This model describes the propagation of an action potential along the axon of a neuron at the scale of ion channels. Mathematically, this model is a fully coupled
A. Genadot, M. Thieullen
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Piecewise Deterministic Markov Processes in Biological Models [PDF]
, 2014 in: Semigroup of Operators - Theory and Applications, J. Banasiak et al. (eds.), Springer Proceedings in Mathematics & Statistics 113, (2015), pp.
Rudnicki, Ryszard, Tyran-Kaminska, Marta
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The Analogue of Bohm-Bell Processes on a Graph [PDF]
, 2005 Bohm-Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes $Q_t$ generalizing in a natural way both Bohm's dynamical system in configuration space for nonrelativistic quantum mechanics and Bell's jump ...
Balachandran +26 more
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Numerical Methods for the Exit Time of a Piecewise-Deterministic Markov Process [PDF]
Advances in Applied Probability, 2010 We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP). Our approach is based on the quantization of an underlying discrete-time Markov chain related to the PDMP.
Adrien Brandejsky +2 more
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On Risk-Sensitive Piecewise Deterministic Markov Decision Processes [PDF]
Applied Mathematics & Optimization, 2018 We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state space is Borel, and the transition and cost rates are locally integrable along the drift.
Guo, Xin, Zhang, Yi
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A piecewise deterministic scaling limit of Lifted Metropolis-Hastings in the Curie-Weiss model [PDF]
, 2016 In Turitsyn, Chertkov, Vucelja (2011) a non-reversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis-Hastings (LMH).
Bierkens, Joris, Roberts, Gareth
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Optimal choice among a class of nonparametric estimators of the jump rate for piecewise-deterministic Markov processes [PDF]
, 2016 A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times.
Azaïs, Romain, Muller-Gueudin, Aurélie
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