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Long-Time Behavior for Subcritical Measure-Valued Branching Processes with Immigration
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures....
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On the Solvability of Initial Problems for Abstract Singular Equations Containing Fractional Derivatives
With the help of integral representations of the Poisson type, it is established that the Cauchy problem for a number of abstract singular equations...
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Special Topic: Piecewise Deterministic Markov Processes in Population Biology
In this chapter a stochastic process is introduced as a model of deterministic population growth subject to independent random disturbances that...
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Introduction and Motivating Examples
Stochastic differential equations, in the sense of Itô, arise quite naturally as mathematical models in many areas of science, engineering and...
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Markov Processes, Transition Functions and Feller Semigroups
In this chapterMarkov process Transition function Feller semigroup we introduce a class of (temporally homogeneous) Markov processes which we will...
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On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes with State-Dependent Jump Intensity
In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion...
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Geometry of generalized fluid flows
The Euler equation of an ideal (i.e. inviscid incompressible) fluid can be regarded, following V. Arnold, as the geodesic flow of the right-invariant
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The Square Root of the Laplacian
In this chapter, we study the simplest integro-differential elliptic operator: the square-root of the Laplacian,...
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Continuous Time Mixed State Branching Processes and Stochastic Equations
A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The process can...
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Independence
In this chapter, we introduce the important probabilistic concept of independence. We establish the famous Borel-Cantelli lemma, and as an...
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Unbiased simulation method with the poisson kernel method for stochastic differential equations with reflection
We consider unbiased simulation methods for one-dimensional stochastic differential equations with reflection at zero. In particular, we propose...
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On the characterization of harmonic functions with initial data in Morrey space
Let ( X, d, μ ) be a metric measure space satisfying the doubling condition and an L 2 -Poincaré inequality. Consider the nonnegative operator
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The work of Hillel Furstenberg and its impact on modern mathematics
In the following article we have attempted to give some account of the extraordinary work of Hillel Furstenberg and its impact on modern mathematics....
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Stability Properties of Mild Solutions of SPDEs Related to Pseudo Differential Equations
This is a review article which presents part of the contribution of Sergio Albeverio to the study of existence and uniqueness of solutions of SPDEs...
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Fluid–Plate Interaction with Kelvin-Voigt Dam** and Bending Moment at the Interface: Well-posedness, Spectral Analysis, Uniform Stability
We consider a fluid-plate interaction model where the two dimensional plate is subject to viscoelastic (strong) dam**, as it occurs in some...
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Elliptic Equations with Translations of General Form in a Half-Space
AbstractWe study the Dirichlet problem in a half-space for elliptic differential-difference equations with operators representing superpositions of...
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Diffusion approximation for a simple kinetic model with asymmetric interface
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant...
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Applications to Dynamical Systems
In this chapter we consider three different classes of unbounded operators that arise in applications. In the first section we consider exponential...