Related papers: Markov processes with free Meixner laws
We consider the Markov random flight $\bold X(t), \; t>0,$ in the three-dimensional Euclidean space $\Bbb R^3$ with constant finite speed $c>0$ and the uniform choice of the initial and each new direction at random time instants that form a…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
Weconsider Markov decision processes arising from a Markov model of an underlying natural phenomenon. Such phenomena are usually periodic (e.g. annual) in time, and so the Markov processes modelling them must be time-inhomogeneous, with…
This is a survey paper about reciprocal processes. The bridges of a Markov process are also Markov. But an arbitrary mixture of these bridges fails to be Markov in general. However, it still enjoys the interesting properties of a reciprocal…
In this article, we consider McKean stochastic differential equations, as well as their corresponding McKean-Vlasov partial differential equations, which admit a unique stationary state, and we study the linearized It\^o diffusion process…
Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…
Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional…
When analysing statistical systems or stochastic processes, it is often interesting to ask how they behave given that some observable takes some prescribed value. This conditioning problem is well understood within the linear operator…
A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over a infinite state space can be identified by a…
Measure-free discrete time stochastic processes in Riesz spaces were formulated and studied by Kuo, Labuschagne and Watson. Aspects relating martingales, stopping times, convergence of these processes as well as various decomposition were…
We study stochastic monotonicity and propagation of order for Markov processes with respect to stochastic integral orders characterized by cones of functions satisfying $\Phi f \geq 0$ for some linear operator $\Phi$. We introduce a new…
In this article we study a homogeneous transient diffusion process $X$. We combine the theories of differential equations and of stochastic processes to obtain new results for homogeneous diffusion processes, generalizing the results of…
We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and…
We prove existence and uniqueness of solutions to Fokker--Planck equations associated to Markov operators multiplicatively perturbed by degenerate time-inhomogeneous coefficients. Precise conditions on the time-inhomogeneous coefficients…
Hawkes processes are a class of simple point processes whose intensity depends on the past history, and is in general non-Markovian. Limit theorems for Hawkes processes in various asymptotic regimes have been studied in the literature. In…