Related papers: Around Ovsyannikov's method
The evolution of baryon density perturbations on very small scales is investigated. In particular, the nonlinear growth induced by the radiation drag force from the shear velocity field on larger scales during the recombination epoch, which…
We provide a new approach to obtain solutions of certain evolution equations set in a Banach space and equipped with nonlocal boundary conditions. From this approach we derive a family of numerical schemes for the approximation of the…
The initial value problem for an evolution equation of type $v' + Av + BKv = f$ is studied, where $A:V_A \to V_A'$ is a monotone, coercive operator and where $B:V_B \to V_B'$ induces an inner product. The Banach space $V_A$ is not required…
The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. Finding the steady state probability…
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…
Known investigations of nonlinear evolution equations $${dx\over dt} + A(t)x(t) = f(t)\ ,\quad x(t_{0}) = x^{0},\ \quad t_{0} \le t < \infty\ , \eqno(0.1)$$ with monotone operators $A(t)$ acting from reflexive Banach space $B$ to dual space…
A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…
Assume that a block operator of the form $\left(\begin{smallmatrix}A_{1}\\A_{2}\quad 0\end{smallmatrix}\right)$, acting on the Banach space $X_{1}\times X_{2}$, generates a contraction $C_{0}$-semigroup. We show that the operator $A_{S}$…
Using backward propagators, we construct inhomogeneous Random Evolutions on Banach spaces driven by (uniformly ergodic) Semi-Markov processes. After studying some of their properties (measurability, continuity, integral representation), we…
The aim of this paper is to prove the strong law of large numbers (SLLN) as well as the central limit theorem (CLT) for a class of vector-valued stochastic processes which arise as solutions of the stochastic evolution inclusion…
We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…
Existence and uniqueness of mild solutions to a class of semilinear stochastic evolution equations with additive noise is proved. The linear part of the drift term is the generator of a compact semigroup of contractions, while the nonlinear…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
We consider a Backward Stochastic Differential Equation (BSDE for short) in a Markovian framework for the pair of processes $(Y,Z)$, with generator with quadratic growth with respect to $Z$. The forward equation is an evolution equation in…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…
This paper is devoted to the existence, uniqueness and comparison theorem on unbounded solutions of one-dimensional backward stochastic differential equations (BSDEs) with sub-quadratic generators, where the terminal time is allowed to be…
Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the…
In this paper we study a nonlinear size-structured population model with distributed delay in the recruitment. The delayed problem is reduced into an abstract initial value problem of an ordinary differential equation in the Banach space by…
It is well known that the non-autonomous scalar differential equation of evolution has a unique solution given by an elementary exponential function. In general there is no such analogous solution to the corresponding non-autonomous…