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1.
A. M. Kulik 《Ukrainian Mathematical Journal》2004,56(5):774-789
We determine generalized diffusion coefficients and describe the structure of local times for a process defined as a solution of a one-dimensional stochastic differential equation with singular drift coefficient.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 642–655, May, 2004. 相似文献
2.
This article continues the study of Liu [Statist. Probab. Lett. 78(2008): 1775–1783; Stoch. Anal. Appl. 29(2011): 799–823] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a consequence, the associated stochastic equations have unbounded operators acting on the point or distributed delayed terms, while the operator acting on the instantaneous term generates a strongly continuous semigroup. We present conditions on the delay systems to obtain a unique stationary solution by combining spectrum analysis of unbounded operators and stochastic calculus. A few instructive cases are analyzed in detail to clarify the underlying complexity in the study of systems with unbounded delayed operators. 相似文献
3.
Richard B. Sowers 《Transactions of the American Mathematical Society》2001,353(4):1321-1334
We investigate the behavior of the tangent flow of a stochastic differential equation with a fast drift. The state space of the stochastic differential equation is the two-dimensional cylinder. The fast drift has closed orbits, and we assume that the orbit times vary nontrivially with the axial coordinate. Under a nondegeneracy assumption, we find the rate of growth of the tangent flow. The calculations involve a transformation introduced by Pinsky and Wihstutz.
4.
M. Almazov 《Journal of Mathematical Sciences》1993,63(4):484-489
The explicit form of the transition density is determined for the solution (t) of the stochastic diffusion equation d(t)=a((t))dt+dw(t), where a(z)= for x [a, b] and a(x)=0 for x [a, b], w(t) is a Wiener process.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 99–105, 1987. 相似文献
5.
Tubaro Luciano 《随机分析与应用》2013,31(2):205-214
A multi–operative Markovian machine interference model with arbitrary inital number of breakdowns is studied by taking mean breakdown of each machine as λ-1 and the mean repairtime of each machine as μ-1. The transient state probabilities of number of breakdowns and initial busy period distributions of a given number of operatives have been obtained in closed form using Laplace transform and matrix theory. The efficacy of the method is tested by computing the state probabilities and measures of effectiveness such as machine availability function and operating efficiency function for various values of traffic intensity ρ=λ/μ. 相似文献
6.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):301-314
In the present work we give general sufficient conditions in terms of Lyapunov functions which ensure existence of a weak solution for a stochastic differential equation for which conditions of existence hold in every bounded region. 相似文献
7.
M. M. Vas’kovskii 《Differential Equations》2013,49(8):925-932
We prove an existence theorem for stochastic hyperbolic equations with measurable locally bounded coefficients. A solution of a stochastic hyperbolic equation is understood as a martingale solution of the stochastic inclusion corresponding to the equation. 相似文献
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9.
On the asymptotic behavior of an unstable solution of an inhomogeneous stochastic diffusion equation
Sufficient conditions are obtained for the normalized trajectories of an unstable solution of the one-dimensional Itô stochastic differential equation with coefficientsa(t, x) and(t, x) to coincide with the normalized trajectories of the solution of the equation with coefficientsa(x) and(x) ast assuming that the coefficientsa(t, x) and(t, x) have a certain average closeness to the coefficientsa(x) and(x) over time ast.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 15, pp. 3–10, 1987. 相似文献
10.
Long Yiming 《数学学报(英文版)》1991,7(4):360-369
An unbounded solution of a Duffing's equation with a smooth superlinear nonlinearity is constructed. 相似文献
11.
We prove newa priori estimates for the resolvent of a minimal quantum dynamical semigroup. These estimates simplify well-known conditions sufficient
for conservativity and impose continuity conditions on the time-dependent operator coefficients ensuring the existence of
conservative solutions of the Markov evolution equations.
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 125–140, January, 1997.
Translated by A. M. Chebotarev 相似文献
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13.
On the long time behavior of the stochastic heat equation 总被引:2,自引:0,他引:2
We consider the stochastic heat equation in one space dimension and compute – for a particular choice of the initial datum
– the exact long time asymptotic. In the Carmona-Molchanov approach to intermittence in non stationary random media this corresponds
to the identification of the sample Lyapunov exponent. Equivalently, by interpreting the solution as the partition function of a directed polymer in a random environment, we obtain
a weak law of large numbers for the quenched free energy. The result agrees with the one obtained in the physical literature
via the replica method. The proof is based on a representation of the solution in terms of the weakly asymmetric exclusion
process.
Received: 11 November 1997 / Revised version: 31 July 1998 相似文献
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15.
The asymptotic behavior of a stochastic process satisfying a linear stochastic differential equation is analyzed. More specifically, the problem is solved of finding a normalizing function such that the normalized process tends to zero with probability 1. The explicit expression found for the function involves the parameters of the perturbing process, and the function itself has a simple interpretation. The solution of the indicated problem makes it possible to considerably improve almost sure optimality results for a stochastic linear regulator on an infinite time interval. 相似文献
16.
By using the Krylov estimate, we prove the exponential ergodicity of the invariant measure for stochastic Langevin equation with singular coefficients, where the classical Lyapunov condition cannot be verified. 相似文献
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18.
Giorgio Metafune Diego Pallara 《Journal of Mathematical Analysis and Applications》2011,377(1):170-179
Given a second-order elliptic operator on Rd, with bounded diffusion coefficients and unbounded drift, which is the generator of a strongly continuous semigroup on L2(Rd) represented by an integral, we study the time behavior of the integral kernel and prove estimates on its decay at infinity. If the diffusion coefficients are symmetric, a local lower estimate is also proved. 相似文献
19.
Thomas Strömberg 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1802-1811
We present comparison, uniqueness and existence results for unbounded solutions of a viscous Hamilton-Jacobi or eikonal equation. The equation includes an unbounded potential term V(x) subject to a quadratic upper bound. The results are obtained through a tailor-made change of variables in combination with the Hopf-Cole transformation. An integral representation formula for the solution of the Cauchy problem is derived in the case where V(x)=ω2|x|2/2. 相似文献
20.
Franco Fagnola 《Probability Theory and Related Fields》1990,86(4):501-516
Summary We prove an existence, uniqueness and unitarity theorem for quantum stochastic differential equations with unbounded coefficients which satisfy an analyticity condition on a common dense invariant domain. This result, applied to the quantum harmonic oscillator, gives a rigorous meaning to a large class of stochastic differential equations that have been considered formally in quantum probability. 相似文献