Related papers: Branching processes and Koenigs function
Inhomogeneous Kirchhoff type equations with indefinite data are considered. Some necessary and sufficient conditions for the existence of positive solutions of the problem under consideration are presented.
The asymptotic expansion of the Korteweg-de Vries-Burgers equation is presented in this paper.
It is shown that the curvature function satisfies a nonlinear evolution equation under the general curve shortening flow and a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time.
Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with…
We give a stochastic model for the fragmentation phase of a snow avalanche. We construct a fragmentation-branching process related to the avalanches, on the set of all fragmentation sizes introduced by J. Bertoin. A fractal property of this…
For branching processes, the generating functions for limit distributions of so-called ratios of probabilities of rare events satisfy the Schr\"oder-type integral-functional equations. Excepting limited special cases, the corresponding…
A simple expression for the non-equilibrium distribution function in ultra-fast transient processes is proposed. Postulating its dependence on temporal derivatives of the equilibrium integrals of motion, non-equilibrium analogues of the…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
The Cauchy problem for the Burgers equation and the Korteweg-de Vries equation is considered. Uniform renormalized asymptotic solutions are constructed in cases of a large initial gradient and a perturbed initial weak discontinuity.
In this paper we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process. \beqnn X_t \ar=\ar x+\int_0^t\gamma_0(X_s)\dd…
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…
A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time-space noises. The family can be regarded as an inhomogeneous increasing path-valued…
By means of non-smooth critical point theory we obtain existence of infinitely many weak solutions of the fractional Schr\"odinger equation with logarithmic nonlinearity. We also investigate the H\"older regularity of the weak solutions.
In this paper we introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not L\'evy processes, they somehow generalize subordinators in the sense that their Laplace exponents are…
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…
In this note, we present a version of Hoeffding's inequality in a continuous-time setting, where the data stream comes from a uniformly ergodic diffusion process. Similar to the well-studied case of Hoeffding's inequality for discrete-time…
We establish limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems in $\R^d$ with anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit…
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a new time discretisation of…