The Experts below are selected from a list of 503985 Experts worldwide ranked by ideXlab platform
Pierre Vallois - One of the best experts on this subject based on the ideXlab platform.
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m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index
Annales de l'IHP - Probabilités et Statistiques, 2005Co-Authors: Mihai Gradinaru, Ivan Nourdin, Francesco Russo, Pierre ValloisAbstract:Given an integer m, a probability measure ν on [0,1], a process X and a Real Function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the fractional Brownian motion B, for any locally bounded Function g, the corresponding integral vanishes for all odd indices m>1/2H and any symmetric ν. One consequence is an Itô–Stratonovich type expansion for the fractional Brownian motion with arbitrary Hurst index 01/6.
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Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4
Annals of Probability, 2003Co-Authors: Mihai Gradinaru, Francesco Russo, Pierre ValloisAbstract:Given a locally bounded Real Function g, we examine the existence of a 4-covariation $[g(B^H), B^H, B^H, B^H]$, where $B^H$ is a fractional Brownian motion with a Hurst index $H \ge \tfrac{1}{4}$. We provide two essential applications. First, we relate the 4-covariation to one expression involving the derivative of local time, in the case $H = \tfrac{1}{4}$, generalizing an identity of Bouleau--Yor type, well known for the classical Brownian motion. A second application is an Itô formula of Stratonovich type for $f(B^H)$. The main difficulty comes from the fact $B^H$ has only a finite 4-variation.
Francesca Gladiali - One of the best experts on this subject based on the ideXlab platform.
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on a singular eigenvalue problem and its applications in computing the morse index of solutions to semilinear pde s
Nonlinear Analysis-real World Applications, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:Abstract We investigate nodal radial solutions to semilinear problems of type − Δ u = f ( | x | , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded radially symmetric domain of R N ( N ≥ 2 ) and f is a Real Function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenFunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.
Mihai Gradinaru - One of the best experts on this subject based on the ideXlab platform.
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m-order integrals and generalized Ito's formula; the case of a fractional Brownian motion with any Hurst index
Annales de l'IHP - Probabilités et Statistiques, 2005Co-Authors: Mihai Gradinaru, Ivan Nourdin, Francesco Russo, Pierre ValloisAbstract:Given an integer m, a probability measure ν on [0,1], a process X and a Real Function g, we define the m-order ν-integral having as integrator X and as integrand g(X). In the case of the fractional Brownian motion B, for any locally bounded Function g, the corresponding integral vanishes for all odd indices m>1/2H and any symmetric ν. One consequence is an Itô–Stratonovich type expansion for the fractional Brownian motion with arbitrary Hurst index 01/6.
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Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index H>=1/4
Annals of Probability, 2003Co-Authors: Mihai Gradinaru, Francesco Russo, Pierre ValloisAbstract:Given a locally bounded Real Function g, we examine the existence of a 4-covariation $[g(B^H), B^H, B^H, B^H]$, where $B^H$ is a fractional Brownian motion with a Hurst index $H \ge \tfrac{1}{4}$. We provide two essential applications. First, we relate the 4-covariation to one expression involving the derivative of local time, in the case $H = \tfrac{1}{4}$, generalizing an identity of Bouleau--Yor type, well known for the classical Brownian motion. A second application is an Itô formula of Stratonovich type for $f(B^H)$. The main difficulty comes from the fact $B^H$ has only a finite 4-variation.
Minbo Yang - One of the best experts on this subject based on the ideXlab platform.
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existence and concentration of ground state solutions for a critical nonlocal schrodinger equation in r2
Journal of Differential Equations, 2016Co-Authors: Claudianor O Alves, Daniele Cassani, Cristina Tarsi, Minbo YangAbstract:We study the following singularly perturbed nonlocal Schrodinger equation −e2Δu+V(x)u=eμ−2[1|x|μ⁎F(u)]f(u)inR2, where V(x) is a continuous Real Function on R2, F(s) is the primitive of f(s), 0<μ<2 and e is a positive parameter. Assuming that the nonlinearity f(s) has critical exponential growth in the sense of Trudinger–Moser, we establish the existence and concentration of solutions by variational methods.
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investigating the multiplicity and concentration behaviour of solutions for a quasi linear choquard equation via the penalization method
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2016Co-Authors: Claudianor O Alves, Minbo YangAbstract:We study the multiplicity and concentration behaviour of positive solutions for a quasi-linear Choquard equation where Δ p is the p -Laplacian operator, 1 p N , V is a continuous Real Function on ℝ N , 0 μ N , F ( s ) is the primitive Function of f ( s ), e is a positive parameter and * represents the convolution between two Functions. The question of the existence of semiclassical solutions for the semilinear case p = 2 has recently been posed by Ambrosetti and Malchiodi. We suppose that the potential satisfies the condition introduced by del Pino and Felmer, i.e. V has a local minimum. We prove the existence, multiplicity and concentration of solutions for the equation by the penalization method and Lyusternik–Schnirelmann theory and even show novel results for the semilinear case p = 2.
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existence and concentration of ground state solutions for a critical nonlocal schr odinger equation in r 2
arXiv: Analysis of PDEs, 2016Co-Authors: Claudianor O Alves, Daniele Cassani, Cristina Tarsi, Minbo YangAbstract:We study the following singularly perturbed nonlocal Schr\"{o}dinger equation $$ -\vr^2\Delta u +V(x)u =\vr^{\mu-2}\Big[\frac{1}{|x|^{\mu}}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, $$ where $V(x)$ is a continuous Real Function on $\R^2$, $F(s)$ is the primitive of $f(s)$, $0<\mu<2$ and $\vr$ is a positive parameter. Assuming that the nonlinearity $f(s)$ has critical exponential growth in the sense of Trudinger-Moser, we establish the existence and concentration of solutions by variational methods.
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existence of solutions for a nonlinear choquard equation with potential vanishing at infinity
arXiv: Analysis of PDEs, 2015Co-Authors: Claudianor O Alves, Giovany M Figueiredo, Minbo YangAbstract:We study the following class of nonlinear Choquard equation, $$ -\Delta u +V(x)u =\Big( \frac{1}{|x|^\mu}\ast F(u)\Big)f(u) \quad \mbox{in} \quad \R^N, $$ where $0<\mu
Anna Lisa Amadori - One of the best experts on this subject based on the ideXlab platform.
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on a singular eigenvalue problem and its applications in computing the morse index of solutions to semilinear pde s
Nonlinear Analysis-real World Applications, 2020Co-Authors: Anna Lisa Amadori, Francesca GladialiAbstract:Abstract We investigate nodal radial solutions to semilinear problems of type − Δ u = f ( | x | , u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded radially symmetric domain of R N ( N ≥ 2 ) and f is a Real Function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, which is studied in full detail. The presented approach also describes the symmetries of the eigenFunctions. This characterization enables to give a lower bound for the Morse index in a forthcoming work.
