Related papers: Bi-Poisson process
We introduce Markov substitute processes, a new model at the crossroad of statistics and formal grammars, and prove its main property : Markov substitute processes with a given support form an exponential family.
We analyze certain stationary fields with linear regressions and quadratic conditional variances. This classic probabilistic problem leads somewhat unexpectedly to stationary Markov processes closely tied to non-commutative probability…
In this paper we introduce a method for resolving multi-parameter likelihoods by fixing all parameter values, but two. Evaluation of those two variables is followed by iteratively cycling through each of the parameters in turn until…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…
A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
We propose to study a new type of Backward stochastic differential equations driven by a family of It\^o's processes. We prove existence and uniqueness of the solution, and investigate stability and comparison theorem.
In this paper we present the classical results of Kolmogorov's backward and forward equations to the case of a two-parameter Markov process. These equations relates the infinitesimal transition matrix of the two-parameter Markov process.…
We consider matrix-valued processes described as solutions to stochastic differential equations of very general form. We study the family of the empirical measure-valued processes constructed from the corresponding eigenvalues. We show that…
We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation…
We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…
We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…
In this paper, the weak convergence of additive functionals of processes with locally independent increments and with Markov switching in the scheme of Poisson approximation is proved. For the relative compactness, a method proposed by R.…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We study linear statistics of a class of determinantal processes which interpolate between Poisson and GUE/Ginibre statistics in dimension 1 or 2. These processes are obtained by performing an independent Bernoulli percolation on the…
In this paper we propose a (sub)distribution-based bisimulation for labelled Markov processes and compare it with earlier definitions of state and event bisimulation, which both only compare states. In contrast to those state-based…
From the point of view of stochastic analysis the Caputo and Riemann-Liouville derivatives of order $\al \in (0,2)$ can be viewed as (regularized) generators of stable L\'evy motions interrupted on crossing a boundary. This interpretation…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…