共查询到20条相似文献,搜索用时 15 毫秒
1.
Yves Le Jan 《Probability Theory and Related Fields》1985,70(4):609-620
Summary This paper includes a detailed study of isotropic brownian motion on matrices and brownian flows associated with isotropic gaussian fields. Characteristic exponents, stability, asymptotic behaviour, statistical equilibrium are the topics on which the main results are obtained. 相似文献
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In this paper it is shown that under some very mild and natural conditions the Riemannian submersion of Brownian motion is an autonomous diffusion with a drift proportional to the mean curvature of the fibres. Interpreting Brownian motion as the limit of a geodesic random walk enables us to give a natural explanation of this result 相似文献
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Let M be a Cartan-Hadamard manifold of dimension d ≧ 3, let p ? M and x = exp {r(x)θ(x)} be geodesic polar coordinates with pole p and let X be the Brownian motion on M. Let SectM(x) denote the sectional curvature of any plane section in Mx. We prove that for each c > 2, there is a 0 < β < 1 such that if - L2r(x)2β ≦ SectM(x) ≦ -cr(x)?2 for all x in the complement of a compact set, then limt → ∞ θ(Xt) exists a.s. and defines a nontrivial invariant random variable. The Dirichlet problem at infinity and a conjecture of Greene and Wu are also discussed. 相似文献
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This work is concerned with the existence and uniqueness of a strong Markov process that has continuous sample paths and the following additional properties:
- (i) The state space is an infinite two-dimensional wedge, and the process behaves in the interior of the wedge like an ordinary Brownian motion.
- (ii) The process reflects instantaneously at the boundary of the wedge, the angle of reflection being constant along each side.
- (iii) The amount of time that the process spends at the comer of the wedge is zero (i.e., the set of times for which the process is at the comer has Lebesgue measure zero).
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In this paper, we study a multi-dimensional backward stochastic differential equation (BSDE) with oblique reflection, which is a BSDE reflected on the boundary of a special unbounded convex domain along an oblique direction, and which arises naturally in the study of optimal switching problem. The existence of the adapted solution is obtained by the penalization method, the monotone convergence, and the a priori estimates. The uniqueness is obtained by a verification method (the first component of any adapted solution is shown to be the vector value of a switching problem for BSDEs). As applications, we apply the above results to solve the optimal switching problem for stochastic differential equations of functional type, and we give also a probabilistic interpretation of the viscosity solution to a system of variational inequalities. 相似文献
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We examine the connections between a novel class of multi-person stopping games with redistribution of payoffs and multi-dimensional reflected BSDEs in discrete- and continuous-time frameworks. Our goal is to provide an essential extension of classic results for two-player stopping games (Dynkin games) to the multi-player framework. We show the link between certain multi-period m-player stopping games and a new kind of m-dimensional reflected BSDEs. The existence and uniqueness of a solution to continuous-time reflected BSDEs are established. Continuous-time redistribution games are constructed with the help of reflected BSDEs and a characterization of the value of such stopping games is provided. 相似文献
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Small‐amplitude expansions are utilized to discuss the mean flow induced by the reflection of a weakly nonlinear internal gravity wave beam at a uniform rigid slope, in the case where the beam planes of constant phase meet the slope at an arbitrary direction, not necessarily parallel to the isobaths, and the flow cannot be taken as two dimensional. Along the vertical, the Eulerian mean flow, due to such an oblique reflection, is equal and opposite to the Stokes drift so the Lagrangian mean flow vanishes, similar to a two‐dimensional reflection. The horizontal Eulerian mean flow, however, is controlled by the mean potential vorticity (PV) and the corresponding Lagrangian mean flow is generally nonzero, in contrast to two‐dimensional flow where PV identically vanishes. For an oblique reflection, furthermore, viscous dissipation can trigger generation of horizontal mean flow via irreversible production of mean PV, a phenomenon akin to streaming. 相似文献
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A. W. Marris 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1982,33(1):124-131
Summary It is proved that the only isochoric circulation-preserving motions whose vorticity is steady, lamellar and bears a constant magnitude on a vortex-line are (1) plane motions of constant vorticity (on which certain unsteady potential motions may be superposed), and (2) a particular circular-helical motion.
Zusammenfassung Es wird bewiesen, daß die einzigen isochoren Bewegungen mit Erhaltung der Zirkulation, deren Rotation zeitunabhängig lamellar und konstant entlang einer Wirbellinie ist, die folgenden sind: 1. Ebene Bewegung mit konstanter Rotation, der gewisse zeitabhängige Potentialbewegungen überlagert werden können; 2. eine besondere Kreis-Schrauben-Bewegung.相似文献
11.
A. Askari Hemmat Jean-Pierre Gabardo 《Journal of Mathematical Analysis and Applications》2009,356(1):346-922
Gramian analysis is used to study properties of a shift-invariant system , where B is an invertible n×n matrix and Φ a finite or countable subset of L2(Rn) under the assumption that the system forms a frame for the closed subspace M of L2(Rn). In particular, the relationship between various features of such system, such as being a frame for the whole space L2(Rn), being a Riesz sequence and having a unique shift-generated dual of type I or II is discussed in details. Several interesting examples are presented. 相似文献
12.
M. Shashiashvili 《Georgian Mathematical Journal》1996,3(2):153-176
The Skorokhod oblique reflection problem is studied in the case ofn-dimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness of the solution. The continuity of the corresponding solution mapping is established. This property enables one to construct in a direct way the reflected (in a convex polyhedral domain) diffusion processes possessing the nice properties. 相似文献
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Harry Kesten 《Stochastic Processes and their Applications》1978,7(1):9-47
We consider a branching diffusion {Zt}t?0 in which particles move during their life time according to a Brownian motion with drift -μ and variance coefficient σ2, and in which each particle which enters the negative half line is instantaneously removed from the population. If particles die with probability c dt+o(dt) in [t,t+dt] and if the mean number of offspring per particle is m>1, then Zt dies out w.p.l. if . If μ<μ0, then itZt grows exponentially with positive probability. Our main concern here is with the critical case where μ=μ0. Even though in this case, we find that is only exp, and conditionally on {ZT>0} there are with high probability much fewer particles alive at time T than . 相似文献
15.
A Kalman type system of integral equations is obtained for the linear filtering problem in which the noise generating the signal is a fractional Brownian motion with long-range dependence. The error in applying the usual Kalman filter to this problem is determined explicitly for a simple example 相似文献
16.
Elhadi Ait Dads Safoua Khelifi Mohsen Miraoui 《Mathematical Methods in the Applied Sciences》2020,43(17):10262-10275
In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed-point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general-type reflection integro-differential equations. We suppose that the nonlinear part is measure pseudo almost automorphic and in which we distinguish the two constant and variable cases for the Lipschitz coefficients of the functions associated with this part. It is assumed that the linear part of the equation considered admits an exponential dichotomy. Finally, an application is given on the very interesting model of Markus and Yamabe. 相似文献
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《Journal of Applied Mathematics and Mechanics》1998,62(3):351-358
Mechanical systems with a finite number of degrees of freedom, subject to one or more unilateral geometric constraints, are considered. Apart from the main forms of motion—flying, supported motion and non-degenerate collisions—such systems also show more complex, discontinuous motions, including infinitely many impacts in any neighbourhood of the starting time. These motions are possible not only when no continuous motions exist, but also together with continuous motions [1]. It is proved that, in the case of ideal constraints, if the reactions of the constraints at the starting time are non-zero, there cannot be any discontinuous motion. In systems with dry friction there is yet another type of discontinuity, namely, tangential impact at zero approach velocity. Sufficient conditions for continuity of the motion are derived for this case also. The conditions are verified with examples that use the usual models of impact. 相似文献
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For Brownian motion B denote by Bδ its polygonal approximation corresponding to a partition δ of [0,1]. It is proved that if E(f1|Xt|p dt<∞ for some p>2 then converges to in mean as the mesh |Δ|→0 provided the symmetric (Stratonovich) stochastic integral is determined (in the sense given in [4]) 相似文献