共查询到20条相似文献,搜索用时 31 毫秒
1.
Jérémie Unterberger 《Stochastic Processes and their Applications》2018,128(12):4104-4153
We study in this article the hydrodynamic limit in themacroscopic regime of the coupled system of stochastic differential equations,
(0.1)
with , sometimes called generalized Dyson’s Brownian motion, describing the dissipative dynamics of a log-gas of equal charges with equilibrium measure corresponding to a -ensemble, with sufficiently regular convex potential . The limit is known to satisfy a mean-field Mc-Kean–Vlasov equation. We prove that, for suitable initial conditions, fluctuations around the limit are Gaussian and satisfy an explicit PDE.The proof is very much indebted to the harmonic potential case treated in Israelsson (2001). Our key argument consists in showing that the time-evolution generator may be written in the form of a transport operator on the upper half-plane, plus a bounded non-local operator interpreted in terms of a signed jump process. 相似文献
2.
3.
Ercan Sönmez 《Stochastic Processes and their Applications》2018,128(2):426-444
Let be a multivariate operator-self-similar random field with values in . Such fields were introduced in [22] and satisfy the scaling property for all , where is a real matrix and is an real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of and as well as the multiplicity of the eigenvalues of and . 相似文献
4.
Gerd Grubb 《Journal of Functional Analysis》2018,274(9):2634-2660
This work contributes in two areas, with sharp results, to the current investigation of regularity of solutions of heat equations with a nonlocal operator P:
(*)
1) For strongly elliptic pseudodifferential operators (ψdo's) P on of order , a symbol calculus on is introduced that allows showing optimal regularity results, globally over and locally over : for , . The are anisotropic Sobolev spaces of Bessel-potential type, and there is a similar result for Besov spaces.2) Let Ω be smooth bounded, and let P equal (), or its generalizations to singular integral operators with regular kernels, generating stable Lévy processes. With the Dirichlet condition , the initial condition , and , (*) has a unique solution with . Here if , and is contained in if , but contains nontrivial elements from if (where ). The interior regularity of u is lifted when f is more smooth. 相似文献
5.
For Toeplitz operators acting on the weighted Fock space , we consider the semi-commutator , where is a certain weight parameter that may be interpreted as Planck's constant ? in Rieffel's deformation quantization. In particular, we are interested in the semi-classical limit
()
It is well-known that tends to 0 under certain smoothness assumptions imposed on f and g. This result was recently extended to by Bauer and Coburn. We now further generalize (?) to (not necessarily bounded) uniformly continuous functions and symbols in the algebra of bounded functions having vanishing mean oscillation on . Our approach is based on the algebraic identity , where denotes the Hankel operator corresponding to the symbol g, and norm estimates in terms of the (weighted) heat transform. As a consequence, only f (or likewise only g) has to be contained in one of the above classes for (?) to vanish. For g we only have to impose , e.g. . We prove that the set of all symbols with the property that for all coincides with . Additionally, we show that holds for all . Finally, we present new examples, including bounded smooth functions, where (?) does not vanish. 相似文献
6.
7.
Umut Çetin 《Stochastic Processes and their Applications》2018,128(10):3439-3465
Let be a regular one-dimensional transient diffusion and be its local time at . The stochastic differential equation (SDE) whose solution corresponds to the process conditioned on for a given is constructed and a new path decomposition result for transient diffusions is given. In the course of the construction Bessel-type motions as well as their SDE representations are studied. Moreover, the Engelbert–Schmidt theory for the weak solutions of one dimensional SDEs is extended to the case when the initial condition is an entrance boundary for the diffusion. This extension was necessary for the construction of the Bessel-type motion which played an essential part in the SDE representation of conditioned on . 相似文献
8.
For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion on and the slit motion . The diffusion coefficient and drift coefficient of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as . We introduce a function measuring the discrepancy of a standard slit domain from relative to BMD. We show that enjoys a locality property. 相似文献
9.
《Annals of Pure and Applied Logic》2014,165(2):609-619
10.
For any polynomial f of we introduce the following characteristic of the distribution of its second order derivative, which extends the differential uniformity notion: where is the second order derivative. Our purpose is to prove a density theorem relative to this quantity, which is an analogue of a density theorem proved by Voloch for the differential uniformity. 相似文献
11.
12.
《Stochastic Processes and their Applications》2005,115(6):983-1016
We work out a stationary process on the real line to represent the positions of the multiple cracks which are observed in some composites materials submitted to a fixed unidirectional stress . Our model is the one-dimensional random sequential adsorption. We calculate the intensity of the process and the distribution of the inter-crack distance in the Palm sense. Moreover, the successive crack positions of the one-sided process (denoted by , ) are described. We prove that the sequence is a “conditional renewal process”, where is the value of the stress at which forms. The approaches “in the Palm sense” and “one-sided process” merge when . The saturation case is also investigated. 相似文献
13.
Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations
Ravi P. Agarwal Bruno de Andrade Claudio Cuevas 《Nonlinear Analysis: Real World Applications》2010,11(5):3532-3554
We study the existence and uniqueness of a weighted pseudo-almost periodic (mild) solution to the semilinear fractional equation , , where is a linear operator of sectorial negative type. This article also deals with the existence of these types of solutions to abstract partial evolution equations. 相似文献
14.
15.
Neel Patel 《Journal of Differential Equations》2018,264(3):1841-1885
We consider continuation criteria for the three-dimensional relativistic Vlasov–Maxwell system. When the particle density, , is compactly supported at , we prove , where and is arbitrarily small, is a continuation criteria. Our continuation criteria is an improvement in the range to the previously best known criteria due to Kunze [7]. We also consider continuation criteria when has noncompact support. In this regime, Luk–Strain [9] proved that is a continuation criteria for . We improve this result to . Finally, we build on another result by Luk–Strain [8]. The authors proved boundedness of momentum support on a fixed two-dimensional plane is a sufficient continuation criteria. We prove the same result even if the plane varies continuously in time. 相似文献
16.
17.
Let be a digraph with n vertices and m arcs without loops and multiarcs. The spectral radius of G is the largest eigenvalue of its adjacency matrix. In this paper, the following sharp bounds on have been obtained.where G is strongly connected and is the average 2-outdegree of vertex . Moreover, each equality holds if and only if G is average 2-outdegree regular or average 2-outdegree semiregular. 相似文献
18.
19.
20.
The neighbor-distinguishing total chromatic number of a graph is the smallest integer such that can be totally colored using colors with a condition that any two adjacent vertices have different sets of colors. In this paper, we give a sufficient and necessary condition for a planar graph with maximum degree 13 to have or . Precisely, we show that if is a planar graph of maximum degree 13, then ; and if and only if contains two adjacent 13-vertices. 相似文献