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Mathematical Machinery
This chapter introduces the necessary mathematical background from the semigroup theory, particularly the Trotter-Kato approximations, analysis and...
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Markov Chains and Potential Theory on Graphs
We briefly review the basic notions of Markovian potential theory in the context of a countable graph equipped with conductances and dam** (or...
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On Classification of Semigroups Associated to Levy Processes
The work is devoted to the study of properties of operator semigroups with kernels that are, in the general case, random process generalized...
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Single Layer Operators for \( \mathcal {L}\) and Estimates for \( \mathcal {L}^{-1}\)
This chapter is needed to prepare the next chapter on uniqueness. We consider the divergence form operator...
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Structures of Independent Immigration
In this chapter we study independent immigration structures associated with MBprocesses. We first give a formulation of the structures using skew...
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Semiflows, Composition Semigroups, and the Approximation of Dirichlet-to-Neumann Semigroups
We present an approximation for the semigroup generated by a multiplicative perturbation of a Dirichlet-to-Neumann operator and more general...
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A fractional osmosis model for image fusion
This paper introduces a novel model for image fusion that is based on a fractional-order osmosis approach. The model incorporates a definition of...
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Infinite delay fractional stochastic integro-differential equations with Poisson jumps of neutral type
This paper addresses the study of nonlinear fractional stochastic neutral integro-differential equations with Poisson jumps and infinite delay in...
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Conservation Properties
In order to extend the operator theory for L to Hardy spaces, we need to guarantee that certain operators f(L) preserve vanishing zeroth moments or...
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Diffusion Approximations of Markovian Solutions to Discontinuous ODEs
In a companion paper, the authors have characterized all deterministic semigroups, and all Markov semigroups, whose trajectories are Carathéodory...
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Diffusion in Media with Membranes and Some Nonlocal Parabolic Problems
We establish the classical solvability of a certain conjugation problem for one-dimensional (with respect to a spatial variable) Kolmogorov backward...
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Discrete Hölder spaces and their characterization via semigroups associated with the discrete Laplacian and kernel estimates
In this paper, we characterize the discrete Hölder spaces by means of the heat and Poisson semigroups associated with the discrete Laplacian. These...
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Optimal Control of Clarke Subdifferential Type Fractional Differential Inclusion with Non-instantaneous Impulses Driven by Poisson Jumps and Its Topological Properties
This article is devoted to studying the topological structure of a solution set for Clarke subdifferential type fractional non-instantaneous...
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On Flett potentials associated with the Laplace–Bessel differential operator
This article introduces new anisotropic wavelet-type transforms generated by the Laplace–Bessel differential operator. Two components generate these...
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Asymptotic Behavior for Multi-scale SDEs with Monotonicity Coefficients Driven by Lévy Processes
In this paper, we study the asymptotic behavior for multi-scale stochastic differential equations driven by Lévy processes. The optimal strong...