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Wick Ordering Associated with the (p, q)-Gaussian White Noise Process
In this paper the quantum decomposition associated with the noncommutative analog of Gaussian white noise processes for the relation of the...
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Differentiability Properties for Boundary Control of Fluid-Structure Interactions of Linear Elasticity with Navier-Stokes Equations with Mixed-Boundary Conditions in a Channel
In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from...
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A Ray–Knight theorem for \(\nabla \phi \) interface models and scaling limits
We introduce a natural measure on bi-infinite random walk trajectories evolving in a time-dependent environment driven by the Langevin dynamics...
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Fractional Gamma Noise Functionals
We construct an infinite dimensional analysis with respect to non-Gaussian measures of fractional Gamma type which we call fractional Gamma noise...
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White noise theory and general improved Kudryashov method for stochastic nonlinear evolution equations with conformable derivatives
The aim of this work is to investigate the Wick-type stochastic nonlinear evolution equations with conformable derivatives. The general Kudryashov...
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Correction to: Two weight Sobolev norm inequalities for smooth Calderón–Zygmund operators and doubling weights
We correct two errors in the paper "Two weight Sobolev norm inequalities for smooth Calderón–Zygmund operators and doubling weights" published in...
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Space-Time Stochastic Calculus and White Noise
In the first part of this paper I give the historical background to my initial interest in stochastic analysis and to the writing of my book...
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Multilinear Smoothing and Local Well-Posedness of a Stochastic Quadratic Nonlinear Schrödinger Equation
In this article, we study a d -dimensional stochastic quadratic nonlinear Schrödinger equation (SNLS), driven by a fractional derivative (of order
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Numerical Modeling and Open-Source Implementation of Variational Partition-of-Unity Localizations of Space-Time Dual-Weighted Residual Estimators for Parabolic Problems
In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are...
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Space-Time Mixed System Formulation of Phase-Field Fracture Optimal Control Problems
In this work, space-time formulations and Galerkin discretizations for phase-field fracture optimal control problems are considered. The fracture...
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Analytic properties of heat equation solutions and reachable sets
There recently has been some interest in the space of functions on an interval satisfying the heat equation for positive time in the interior of this...
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General Transfer Formula for Stochastic Integral with Respect to Multifractional Brownian Motion
In this work we show how results from stochastic integration with respect to multifractional Brownian motion (mBm) can be simply deduced from results...
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The Gaussian Free Field
The Gaussian free field is defined in this chapter and the identity in law between the vertex occupation field of loop ensembles of intensity ½ or 1...
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Towards a Better Understanding of Fractional Brownian Motion and Its Application to Finance
The aim of this work is to first build the underlying theory behind fractional Brownian motion and applying fractional Brownian motion to financial...
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Calderón—Zygmund Operators and Commutators in Spaces of Homogeneous Type: Weighted Inequalities
The recent proof of the sharp weighted bound for Calderón-Zygmund operators has led to much investigation in sharp mixed bounds for operators and...
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Invariant Measures as Probabilistic Tools in the Analysis of Nonlinear ODEs and PDEs
We consider finite and infinite dimensional Hamiltonian systems and note that Gibbs measures are the unique probability measures satisfying an...
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Fractional Brownian Motion
The previous chapters provide empirical evidence that models with stochastic volatility outperform their deterministic counterpart. In Chap....