相关论文: T. E. Harris's contributions to recurrent Markov p…
We study a time-non-homogeneous Markov process which arose from free probability, and which also appeared in the study of stochastic processes with linear regressions and quadratic conditional variances. Our main result is the explicit…
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stochastic calculus for It\^{o} processes. These processes for…
We characterize recurrence and transience of nonnegative multivariate autoregressive processes of order one with random contractive coefficient matrix, of subcritical multitype Galton-Watson branching processes in random environment with…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d.\ cycles. Although we focus on the classical definition, we present a more general definition that allows for some form…
Linear fractional Galton-Watson branching processes in i.i.d.~random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals.…
Non-Archimedean analogs of Markov quasimeasures and stochastic processes are investigated. Thery are used for the development of stochastic antiderivations. The non-Archimedean analog of the It$\hat o$ formula is proved.
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as…
Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling…
We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a new process whose…
This review concerns recent results on the quantitative study of convergence towards the stationary state for spatially inhomogeneous kinetic equations. We focus on analytical results obtained by means of certain probabilistic techniques…
We develop a method of driving a Markov processes through a continuous flow. In particular, at the level of the transition functions we investigate an approach of adding a first order operator to the generator of a Markov process, when the…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making…
The paper is devoted to the existence of integral functionals $\int_0^\infty f(X(t))\,{\mathrm{d}t}$ for several classes of processes in $\mathbb{R}$ with $d\ge 3$. Some examples such as Brownian motion, fractional Brownian motion, compound…
I shall briefly survey the current status on more rigorous studies of chaos in fluids by focusing along the line of chaos phenotypes: sensitive dependence on initial data, and recurrence.
In the article the distributions of overjump functionals for almost semi-continuous processes on a finite irreducible Markov chain are considered.
We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications.