Roland Riachi
13 followers · 13 following · 1212 views
on the atlas — 32
- Quasi-Monte Carlo methods for elliptic PDEswith random coefficients and applications1 savers
- The Concentration of Invariant Measures for Stochastic Dynamical Systems with Locally Lipschitz Continuous Coefficients in R^d1 savers
- On the Functional Levy-Ito Stochastic Calculus1 savers
- Functional Equations for the Stochastic Exponential1 savers
- Lessons from my PhD - Austin Z. Henley2 savers
- Inverse Source Problems for the Stochastic Wave Equations: Far-Field Patterns1 savers
- Density Dependent Singular Stochastic Differential Equations1 savers
- Analysis of Circulant Embedding Methods for Sampling Stationary Random Fields1 savers
- High-Dimensional Gaussian Sampling: A Review and a Unifying Approach Based on a Stochastic Proximal Point Algorithm1 savers
- Partial Recovery and Weak Consistency in the Non-Uniform Hypergraph Stochastic Block Model1 savers
- A Feynman-Kac Approach for the Spatial Derivative of the Solution to the Wick Stochastic Heat Equation Driven by Time Homogeneous White Noise1 savers
- MSR-TR-2009-192.pdf1 savers
- Extending Martingale Measure Stochatic Integral with Applications to Spatially Homogeneous SPDE's1 savers
- Stochastic Partial Differential Equations: Classical and New • Dynamische Systeme / Stochastik • Fachbereich Mathematik und Informatik2 savers
- Comparison principle for stochastic heat equation on Rd1 savers
- Stochastic integrals for spde's: A comparison1 savers
- A Primer on Stochastic Partial Differential Equations2 savers
- Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions1 savers
- [2008.13092] Fundamental Solution to 1D Degenerate Diffusion Equation with Locally Bounded Coefficients1 savers
- The fundamental solution to 1D degenerate diffusion equation with one-sided boundary1 savers
- Hamilton-Jacobi Equations1 savers
- [1707.01415] Machine Learning, Deepest Learning: Statistical Data Assimilation Problems1 savers
- On Degenerate Partial Differential Equations1 savers
- Chaos Expansion of Heat Equations with White Noise Potentials1 savers
- An Introduction to Malliavin Calculus1 savers
- Advanced stochastic analysis1 savers
- Stochastic Heat Equations with General Multiplicative Gaussian Noises: Hölder Continuity and Intermittency1 savers
- Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations1 savers
- Neural Manifold Ordinary Differential Equations1 savers
- Scalable Gradients for Stochastic Differential Equations1 savers
- Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges5 savers
- Classic Fallacies -- All People in Canada are the Same Age4 savers
highlights — 852
W is a cylindrical Wiener process on a separable Hilbert space U
On Pointwise Malliavin Differentiability of Solutions to Semilinear Parabolic SPDEsq > 2 and G ⊂ R d a smooth bounded
On Pointwise Malliavin Differentiability of Solutions to Semilinear Parabolic SPDEsA is the negative generator of an analytic semigroup of contra ctions S on L q ( G )
On Pointwise Malliavin Differentiability of Solutions to Semilinear Parabolic SPDEsdu + Au dt = f ( u ) dt + σ ( u ) B dW ( t )
On Pointwise Malliavin Differentiability of Solutions to Semilinear Parabolic SPDEsproperty of invariant measures { μ ε
The Concentration of Invariant Measures for Stochastic Dynamical Systems with Locally Lipschitz Continuous Coefficients in R^dexit time and the exit location
The Concentration of Invariant Measures for Stochastic Dynamical Systems with Locally Lipschitz Continuous Coefficients in R^dtwo important kinds of properties are extensively studied
The Concentration of Invariant Measures for Stochastic Dynamical Systems with Locally Lipschitz Continuous Coefficients in R^dX is infinitely divisible if and only if its characteristic function can be written as ̂ P X ( ξ ) = exp(Ψ( ξ ))
On Tempered Discrete and Levy White Noisecharacteristic exponent
On Tempered Discrete and Levy White Noisecharacteristic functional
On Tempered Discrete and Levy White NoiseL 0 (Ω) is the space of real random variables endowed with the conver gence in probability
On Tempered Discrete and Levy White Noisegeneralized random process is therefore a linear and conti nuous functional
On Tempered Discrete and Levy White Noisegeneralized random process S
On Tempered Discrete and Levy White NoiseThe topological dual of S ( R ) is the space S ′ ( R ) of tempered generalized function
On Tempered Discrete and Levy White NoiseSchwartz space of rapidly decaying and infinitely smooth functions is denoted by S ( R
On Tempered Discrete and Levy White Noiseframework of generalized functions allows to define func tions with no pointwise interpretation, such as the Dirac impulse δ and all its derivatives
On Tempered Discrete and Levy White Noisetopological dual D ′ ( R ) of D ( R ) is the space of generalized function
On Tempered Discrete and Levy White NoiseD ( R ) be the space of compactly supported and infinitely smooth fun ctions
On Tempered Discrete and Levy White NoiseX n have a common probability density function given by f ( x ) = c ( | x | +1) log 2 ( | x | +2) where c > 0 is such that ∫ R f ( x )d x = 1
On Tempered Discrete and Levy White NoiseNon-Gaussian S α S random variables have an infinite variance: For α < 2 , we actually have that E [ | X 0 | p ] < ∞ if and only if p < α
On Tempered Discrete and Levy White Noisecommon characteristic function of the X n is ̂ P X n ( ξ ) = exp( − γ α | ξ | α )
On Tempered Discrete and Levy White Noisealso have the equivalence X ∈ S ′ ( Z ) a.s. ⇐⇒ ∃ ǫ > 0 , E [ | X 0 | ǫ ] < ∞
On Tempered Discrete and Levy White Noisee have the equivalence X ∈ ℓ ∞ , − 1 /p ( Z ) a.s. ⇐⇒ E [ | X 0 | p ] < ∞
On Tempered Discrete and Levy White Noisesequence X = ( X n ) n ∈ Z of independent and identically distributed (i.i.d.) random variables X n
On Tempered Discrete and Levy White Noisewe provide characterizations of discrete white noises to be localized in the sequence spac es ℓ ∞ ,α ( Z ) and S ′ ( Z
On Tempered Discrete and Levy White NoiseA discrete white noise is a priori in D ′ ( Z )
On Tempered Discrete and Levy White NoiseP ( ∀ n ∈ Z , X n ≤ a n ) = ∏ n ∈ Z P ( X n ≤ a n ) = ∏ n ∈ Z P ( X 0 ≤ a n
On Tempered Discrete and Levy White Noisediscrete white noise
On Tempered Discrete and Levy White Noiseaw of X is characterized by the quantities P X ( { u ∈ D ′ ( Z ) |〈 u,v 〉≤ a } ) = P ( 〈 X,v 〉≤ a ) (6) for any v ∈ D ( Z ) and a ∈
On Tempered Discrete and Levy White NoiseA random sequence is a random element in the space D ′ ( Z
On Tempered Discrete and Levy White Noiseu ∈ S ′ ( Z ) if and only if u : D ( Z ) → R is continuous for the topology induced by S ( Z )
On Tempered Discrete and Levy White Noisetopological dual of S ( Z ) is the space S ′ ( Z ) of tempered sequences
On Tempered Discrete and Levy White NoiseS ( Z ) = ⋂ α ≥ 0 ℓ ∞ ,α ( Z
On Tempered Discrete and Levy White Noiseapidly decaying sequence is denoted by S ( Z )
On Tempered Discrete and Levy White Noiseconverge to 0 if they have a common support K ⊂ Z outside of which they vanish and if the finite-dimensional vectors ( v k [ n ]) n ∈ K converge to
On Tempered Discrete and Levy White Noisewith the locally convex topology
On Tempered Discrete and Levy White NoiseD ′ ( Z ) is the topological dual of D ( Z )
On Tempered Discrete and Levy White NoiseD ′ ( Z ) is the dual of the space D ( Z ) of sequences that have finitely many nonzero elements
On Tempered Discrete and Levy White NoiseWe denote by D ′ ( Z ) the space of all real sequence
On Tempered Discrete and Levy White NoiseThe novelty of ou r result is the connection between a Lévy white noise and the random sequences ( 〈 W,φ ( ·− n ) 〉 ) n ∈
On Tempered Discrete and Levy White Noiseǫ -condition is equivalent to the temperedness of discrete white noises
On Tempered Discrete and Levy White Noisecharacterize the weighted ℓ ∞ -sequence spaces on which an i.i.d. random sequence belongs in terms of its moment propertie
On Tempered Discrete and Levy White Noiseconnection between Lévy white noises and families of i.i.d. random sequences ( i.e. , discrete white noises)
On Tempered Discrete and Levy White Noisenew proof of Th eorem 0
On Tempered Discrete and Levy White NoiseLévy white noise is tempered as soon as it possesses a finite ab solute moment of order ǫ > 0 arbitrarily small, what they called the ǫ -condition .
On Tempered Discrete and Levy White Noiseas random elements of S ′ ( R ) , there Fourier transform is well-defined and they can theref ore be used for stochastic partial differential equations SPDEs
On Tempered Discrete and Levy White NoiseLévy white noises are therefore constructed as random eleme nts in the space D ′ ( R )
On Tempered Discrete and Levy White Noisekey idea is to endow ge neralized function spaces with random structures compatible with their topolog
On Tempered Discrete and Levy White Noiseramework is the stochastic counterpart of th e theory of generalized functions of Laurent Schwartz
On Tempered Discrete and Levy White Noisewe consider the same questions as in Section 2, but for a generalization of the notion of Lévy process, where the “time” parameter is in R d ` , with d ě
Levy Processes and Levy White Noise as Tempered Distributions