共查询到20条相似文献,搜索用时 62 毫秒
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We prove the comparison theorems for scalar stochastic differential equations in the case of different diffusion coefficients. Conditions are given of stability with probability 1 with respect to the trivial solution to stochastic differential equations with random coefficients. The results remain valid for deterministic analogs of stochastic differential equations with symmetric integrals. 相似文献
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THE PATHWISE SOLUTION FOR A CLASS OF QUASILINEAR STOCHASTIC DIFFERENTIAL EQUATION IN BANACH SPACES I
胡耀忠 《数学物理学报(B辑英文版)》1994,(4)
THEPATHWISESOLUTIONFORACLASSOFQUASILINEARSTOCHASTICDIFFERENTIALEQUATIONINBANACHSPACESIHuYaozhong(胡耀忠)(WuhanInst.ofMath.Sci.,C... 相似文献
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Boualem Djehiche 《Journal of Mathematical Analysis and Applications》2011,384(1):63-69
In this note, nonlinear stochastic partial differential equations (SPDEs) with continuous coefficients are studied. Via the solutions of backward doubly stochastic differential equations (BDSDEs) with continuous coefficients, we provide an existence result of stochastic viscosity sub- and super-solutions to this class of SPDEs. Under some stronger conditions, we prove the existence of stochastic viscosity solutions. 相似文献
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本文研究了非Lipschitz条件下半鞅随机微分方程.利用It(o)分析和Gronwall不等式,探讨了随机微分方程无爆炸解,并证明了随机微分方程解的唯一性. 相似文献
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The existence of insensitizing controls for a forward stochastic heat equation is considered. To develop the duality, we obtain observability estimates for linear forward and backward coupled stochastic heat equations with general coefficients, by means of some global Carleman estimates. Furthermore, the constant in the observability inequality is estimated by an explicit function of the norm of the involved coefficients in the equation. As far as we know, our paper is the first one to address the problem of insensitizing controls for stochastic partial differential equations. 相似文献
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The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions. 相似文献
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We propose a new method viz., using stochastic partial differential equations to study the pathwise uniqueness of stochastic (ordinary) differential equations. We prove the existence and pathwise uniqueness of a class of stochastic differential equations with coefficients in suitable Hermite-Sobolev class using our approach. 相似文献
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该文研究了非Lipschitz条件下的倒向重随机微分方程, 给出了此类方程解的存在唯一性 定理, 推广Pardoux和Peng 1994年的结论; 同时也得到了此类方程在非Lipschitz条件下的比较定理, 推广了Shi,Gu和Liu 2005年的结果. 从而推广倒向重随机微分方程在随机控制和随机偏微分方程在 粘性解方面的应用. 相似文献
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Shaoqin ZHANG 《Frontiers of Mathematics in China》2016,11(2):461-496
Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F.-Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established. 相似文献
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D. G. Korenevskii 《Ukrainian Mathematical Journal》2000,52(2):260-266
We establish the relationship (equivalence) between the spectral and algebraic (coefficient) criteria (the latter is represented in terms of the Sylvester matrix algebraic equation) of mean-square asymptotic stability for three classes of systems of linear equations with varying random perturbations of coefficients, namely, the ltô differential stochastic equations, difference stochastic equations with discrete time, and difference stochastic equations with continuous time. 相似文献
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Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well
understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. However, the
important case of superlinearly growing coefficients has remained an open question. The main difficulty is that numerically
weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty
and establish convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations
whose drift functions have at most polynomial growth. 相似文献
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V.N. Kolokol'tsov A.E. Tyukov 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):1-45
The paper is devoted to the study of stochastic heat equations driven by Lévy noise. Applying the WKB method, we obtain multiplicative small time and semiclassical asymptotics for the Green functions and for solutions of the Cauchy problem for the heat equation under some natural additional assumptions on their coefficients. The first step in this construction consists in solving the corresponding stochastic Hamilton-Jacobi equations which constitute the "classical part" of the semiclassical approximation. In its turn, the corresponding Hamilton-Jacobi equations can be solved via solutions of the corresponding Hamiltonian systems, which gives rise to the method of stochastic characteristics. The relevant theory of stochastic Hamiltonian systems and stochastic Hamilton-Jacobi equations was developed in our previous papers. Here we put the final rung on the ladder: stochastic Hamiltonian systems, stochastic Hamilton-Jacobi equations, stochastic heat equations. 相似文献
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We use Hopf-Lax formula to study local regularity of solution to Hamilton-Jacobi (HJ) equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution to We use Hopf-Lax formula to study local regularity of solution to Hamilton-Jacobi (HJ) equations of multi-dimensional space variables with convex Hamiltonian. Then we give the large time generic form of the solution to HJ equation, i.e. for most initial data there exists a constant T > 0, which depends only on the Hamiltonian and initial datum, for t > T the solution of the IVP (1.1) is smooth except for a smooth n-dimensional hypersurface, across which Du(x, t) is discontinuous. And we show that the hypersurface tends asymptotically to a given hypersurface with rate t 1 4 .HJ equation, i.e. for most initial data there exists a constant T > 0, which depends only on the Hamiltonian and initial datum, for t > T the solution of the IVP (1.1) is smooth except for a smooth n-dimensional hypersurface, across which Du(x, t) is discontinuous. And we show that the hypersurface tends asymptotically to a given hypersurface with rate t-1/4 . 相似文献
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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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The anharmonic oscillator is solved quickly, easily, and elegantly by Adomian's methods for solution of nonlinear stochastic differential equations emphasizing its applicability to nonlinear deterministic equations as well as stochastic equations. No difficulty is encountered in treating the case of the forced anharmonic oscillator or the stochastic case or of any nonlinear oscillating system such as the Duffing or Van der Pol oscillators, for example, with coefficients, as well as forcing functions, which are stochastic processes, since statistical separability is inherent in the Adomian method. 相似文献
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Existence and Uniqueness of Solutions to Time-delays Stochastic Fractional Differential Equations with Non-Lipschitz Coefficients
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In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations. 相似文献
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A. G. Madera 《Applied Mathematical Modelling》1993,17(12):664-668
The unsteady partial differential equations for expectation and correlation distributions of the stochastic temperature distribution in a solid are obtained, when the coefficients and the source term in the stochastic heat transfer equations are white Gaussian processes. Some solutions of the unsteady partial differential equations for expectation and correlation distributions of stochastic heat transfer are presented. 相似文献
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A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential
equations with constant bounded coefficients. 相似文献