Max-plus stochastic processes are counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. In this framework, expectations are linear operations with respect to max-plus arithmetic. Max-plus stochastic control problems are considered, in which a minimizing control enters the state dynamics and running cost. The minimum max-plus expected cost is equal t...

Probabilistic inference allows artificial systems to cope with uncertainty, but it can be computationally demanding. Inspired by biological neural systems, stochastic arithmetic modules on reconfigurable hardware can provide massively parallel systems with limited resources. This work presents a framework to automatically implement Bayesian Machines to perform computations using stochastic bits...

The use of stochastic processing hardware and low precision arithmetic in atmospheric models is investigated. Stochastic processors allow hardware-induced faults in calculations, sacrificing bit-reproducibility in exchange for improvements in performance and potentially accuracy and a reduction in power consumption. A similar trade-off is achieved using low precision arithmetic, with improvemen...

The work described in this paper explores the use of Poisson point processes and stochastic arithmetic to perform signal processing functions. Our work is inspired by the asynchrony and fault tolerance of biological neural systems. The essence of our approach is to code the input signal as the rate parameter of a Poisson point process, perform stochastic computing operations on the signal in th...

In practically all real-world planning and scheduling problems one is faced with uncertainty. Usually this uncertainty is abstracted away during the modeling process, such that standard combinatorial optimization algorithms can be used to solve the problem. This abstraction step is necessary, because these algorithms generally cannot deal with uncertainty. In this thesis we study the Vehicle Ro...

We develop accurate analytical pricing formulae for discretely and continuously monitored arithmetic Asian options under general stochastic asset models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. The payoff of the arithmetic Asian option depends on the arithmetic average price of the underlying asset monitored over a pre-...