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Exit problems for one-dimensional Lévy processes are easier when jumps only occur in one direction. In the last few years, this intuition became more precise: we know now that a wide variety of identities for exit problems of spectrally-negative Lévy processes may be ergonomically expressed in terms of two q-harmonic functions (or scale functions or positive martingales) W and Z. The proofs typically require not much more than the strong Markov property, which hold, in principle, for the wider class of spectrally-negative strong Markov processes. This has been established already in particular cases, such as random walks, Markov additive processes, Lévy processes with omega-state-dependent killing, and certain Lévy processes with state dependent drift, and seems to be true for general strong Markov processes, subject to technical conditions. However, computing the functions W and Z is still an open problem outside the Lévy and diffusion classes, even for the simplest risk models with state-dependent parameters (say, Ornstein–Uhlenbeck or Feller branching diffusion with phase-type jumps).

Research & information: general --- Mathematics & science --- Lévy processes --- non-random overshoots --- skip-free random walks --- fluctuation theory --- scale functions --- capital surplus process --- dividend payment --- optimal control --- capital injection constraint --- spectrally negative Lévy processes --- reflected Lévy processes --- first passage --- drawdown process --- spectrally negative process --- dividends --- de Finetti valuation objective --- variational problem --- stochastic control --- optimal dividends --- Parisian ruin --- log-convexity --- barrier strategies --- adjustment coefficient --- logarithmic asymptotics --- quadratic programming problem --- ruin probability --- two-dimensional Brownian motion --- spectrally negative Lévy process --- general tax structure --- first crossing time --- joint Laplace transform --- potential measure --- Laplace transform --- first hitting time --- diffusion-type process --- running maximum and minimum processes --- boundary-value problem --- normal reflection --- Sparre Andersen model --- heavy tails --- completely monotone distributions --- error bounds --- hyperexponential distribution --- reflected Brownian motion --- linear diffusions --- drawdown --- Segerdahl process --- affine coefficients --- spectrally negative Markov process --- hypergeometric functions --- capital injections --- bankruptcy --- reflection and absorption --- Pollaczek–Khinchine formula --- scale function --- Padé approximations --- Laguerre series --- Tricomi–Weeks Laplace inversion

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Exit problems for one-dimensional Lévy processes are easier when jumps only occur in one direction. In the last few years, this intuition became more precise: we know now that a wide variety of identities for exit problems of spectrally-negative Lévy processes may be ergonomically expressed in terms of two q-harmonic functions (or scale functions or positive martingales) W and Z. The proofs typically require not much more than the strong Markov property, which hold, in principle, for the wider class of spectrally-negative strong Markov processes. This has been established already in particular cases, such as random walks, Markov additive processes, Lévy processes with omega-state-dependent killing, and certain Lévy processes with state dependent drift, and seems to be true for general strong Markov processes, subject to technical conditions. However, computing the functions W and Z is still an open problem outside the Lévy and diffusion classes, even for the simplest risk models with state-dependent parameters (say, Ornstein–Uhlenbeck or Feller branching diffusion with phase-type jumps).

Lévy processes --- non-random overshoots --- skip-free random walks --- fluctuation theory --- scale functions --- capital surplus process --- dividend payment --- optimal control --- capital injection constraint --- spectrally negative Lévy processes --- reflected Lévy processes --- first passage --- drawdown process --- spectrally negative process --- dividends --- de Finetti valuation objective --- variational problem --- stochastic control --- optimal dividends --- Parisian ruin --- log-convexity --- barrier strategies --- adjustment coefficient --- logarithmic asymptotics --- quadratic programming problem --- ruin probability --- two-dimensional Brownian motion --- spectrally negative Lévy process --- general tax structure --- first crossing time --- joint Laplace transform --- potential measure --- Laplace transform --- first hitting time --- diffusion-type process --- running maximum and minimum processes --- boundary-value problem --- normal reflection --- Sparre Andersen model --- heavy tails --- completely monotone distributions --- error bounds --- hyperexponential distribution --- reflected Brownian motion --- linear diffusions --- drawdown --- Segerdahl process --- affine coefficients --- spectrally negative Markov process --- hypergeometric functions --- capital injections --- bankruptcy --- reflection and absorption --- Pollaczek–Khinchine formula --- scale function --- Padé approximations --- Laguerre series --- Tricomi–Weeks Laplace inversion

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This book presents the latest solutions in fuel cell (FC) and renewable energy implementation in mobile and stationary applications. The implementation of advanced energy management and optimization strategies are detailed for fuel cell and renewable microgrids, and for the multi-FC stack architecture of FC/electric vehicles to enhance the reliability of these systems and to reduce the costs related to energy production and maintenance. Cyber-security methods based on blockchain technology to increase the resilience of FC renewable hybrid microgrids are also presented. Therefore, this book is for all readers interested in these challenging directions of research.

Technology: general issues --- Energy industries & utilities --- mobile charging station --- electric vehicle --- operational mode --- location-allocation problem --- battery --- capacitor --- differential flatness --- double-layer capacitor --- energy management --- interleaved converter --- nonlinear control --- second order equation --- supercapacitor --- multi-stack --- Polymer Electrolyte Membrane Fuel Cell (PEMFC) --- power electronics --- stability analysis --- microgrid --- LQR-PI control --- grid-tied mode --- current imbalance --- power quality --- genetic algorithms --- renewable energy --- consumer planning --- real-time strategy --- consumption monitoring --- energy storage systems --- renewable energy sources --- dynamic programming --- cascaded multilevel inverter --- photovoltaic --- leakage current --- IoT security --- Internet of Vehicles --- IoV --- connected car --- Blockchain Governance Game --- mixed game --- stochastic model --- fluctuation theory --- 51 percent attack --- double feed induction generator --- grid frequency and amplitude support --- smart grid --- wind technology (WT) --- load frequency control --- optimization issue --- moth flame optimizer (MFO) --- Harris hawks optimizer (HHO) --- fuel economy --- load-following --- switching strategy --- real-time optimization --- fuel cell vehicle --- fuel cell system --- automatic generation control --- controllers --- optimization techniques --- multisource power system --- interconnected power system --- hybrid gravitational with fire fly algorithm --- gravitational search algorithm --- firefly algorithm