论文信息 - Small Ball Asymptotics for the Stochastic Wave Equation ∗ - 字舞流文

Small Ball Asymptotics for the Stochastic Wave Equation ∗

We examine the small ball asymptotics for the weak solution X of the stochastic wave equation ∂X ∂t (t, x)− ∂ X ∂x (t, x) = g(X(t, x)) + f(t, x)dW (t, x) on the real line with deterministic initial conditions.

B. Øksendal | R. Carmona | H. Holden | J. Ubøe | T. Zhang | Andreas Martin

[1] A. V. D. Vaart,et al. Lectures on probability theory and statistics , 2002 .

[2] Q. Shao,et al. Gaussian processes: Inequalities, small ball probabilities and applications , 2001 .

[3] Werner Linde,et al. Approximation, metric entropy and small ball estimates for Gaussian measures , 1999 .

[4] M. Lifshits. Asymptotic behavior of small ball probabilities , 1999 .

[5] James S. Harris,et al. Probability theory and mathematical statistics , 1998 .

[6] Bernt Øksendal,et al. Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach , 1996 .

[7] M. Ledoux,et al. Isoperimetry and Gaussian analysis , 1996 .

[8] Michel Talagrand,et al. The Small Ball Problem for the Brownian Sheet , 1994 .

[9] J. Kuelbs,et al. Metric entropy and the small ball problem for Gaussian measures , 1993 .

[10] M. Talagrand,et al. Probability in Banach Spaces: Isoperimetry and Processes , 1991 .

[11] R. Carmona,et al. Random non-linear wave equations: Smoothness of the solutions , 1988 .

[12] R. Carmona,et al. Random Nonlinear Wave Equations: Propagation of Singularities , 1988 .

[13] École d'été de probabilités de Saint-Flour,et al. École d'été de probabilités de Saint Flour XIV, 1984 , 1986 .

[14] A survey of small ball theorems and problems , 1980 .

[15] W. Walter. Differential- und Integral-Ungleichungen und ihre Anwendung bei Abschätzungs- und Eindeutigkeitsproblemen , 1964 .