Displaying similar documents to “Random coefficients bifurcating autoregressive processes”

Quermass-interaction process with convex compact grains

Kateřina Helisová, Jakub Staněk (2016)

Applications of Mathematics

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The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison...

Hazard rate model and statistical analysis of a compound point process

Petr Volf (2005)

Kybernetika

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A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process...

Pricing bonds and CDS in the model with rating migration induced by a Cox process

Jacek Jakubowski, Mariusz Niewęgłowski (2008)

Banach Center Publications

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We investigate the properties of a rating migration process assuming that it is given by subordination of a discrete time Markov chain and a Cox process. The problem of pricing of defaultable bonds with fractional recovery of par value with rating migration and credit default swaps is considered. As an example of applications of our results, we give an explicit solution to the pricing problem in a model with short rate and intensity processes given by the solution of a two-dimensional...

On cumulative process model and its statistical analysis

Petr Volf (2000)

Kybernetika

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The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator...