相关论文: Bi-Poisson process

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…

We introduce and study a multiparameter Poisson process (MPP). In a particular case, it is observed that the MPP has a unique representation. Its subordination with the multivariate subordinator and inverse subordinator are studied in…

We prove a parametric generalization of the classical Poincare-Perron theorem on stabilizing recurrence relations where we assume that the varying coefficients of a recurrence depend on auxiliary parameters and converge uniformly in these…

We present an investigation of stochastic evolution in which a family of evolution equations in $L^1$ are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP's) on the…

We introduce a family of Markov processes on set partitions with a bounded number of blocks, called Lipschitz partition processes. We construct these processes explicitly by a Poisson point process on the space of Lipschitz continuous maps…

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in R^d and in some cases provide a full characterisation…

We give an elementary construction of a time-invertible Markov process which is discrete except at one instance. The process is one of the quadratic harnesses studied in our previous papers and can be regarded as a random joint of two…

We consider one-dimensional stochastic differential equations with a boundary condition, driven by a Poisson process. We study existence and uniqueness of solutions and the absolute continuity of the law of the solution. In the case when…

We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of linearization of a Poisson pencil. From the algebraic viewpoint,…

We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results…

We consider two independent Gaussian processes that admit a representation in terms of a stochastic integral of a deterministic kernel with respect to a standard Wiener process. In this paper we construct two families of processes, from a…

Assuming uniqueness of the martingale problem for Markov processes of generators $q_t$ in a quadratic family like \[q_t(i,j) = a_t(i) q_0(i,j)^2 + b_t(i) q_0(i,j) - \frac{a_t(i)}{N} \sum_k q_0(i,k)^2,\] where $a_t(i),b_t(i)$ are predictable…

We study the linear filtering problem for systems driven by continuous Gaussian processes with memory described by two parameters. The driving processes have the virtue that they possess stationary increments and simple semimartingale…

Using Bayesian methods for extreme value analysis offers an alternative to frequentist ones, with several advantages such as easily dealing with parametric uncertainty or studying irregular models. However, computations can be challenging…

We study the dynamics of a family of replicator maps, depending on two parameters. Such studies are motivated by the analysis of the dynamics of evolutionary games under selections. From the dynamics viewpoint, we prove the existence of…

Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coefficients have combinatorial significance for many classical…

We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss the existence -- under suitable hypotheses…

In this paper we prove the Poisson Hypothesis for the limiting behavior of the large queueing systems in some simple ("mean-field") cases. We show in particular that the corresponding dynamical systems, defined by the non-linear Markov…

In the paper we consider a generalizations of the notion of Poisson process to the case when classical convolution is replaced by generalized convolution in the sense of K. Urbanik [16] following two classical definitions of Poisson…