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Communications in Statistics - Theory and Methods, ISSN 0361-0926, 10/2018, Volume 47, Issue 20, pp. 5013 - 5028
For a type of strongly dependent isotropic Gaussian random fields introduced by Mittal (1976), the joint limiting distribution of the maximum and the sum for... 
Discretization | Primary 62G70 | isotropic | Secondary 60G60 | maximum | Gaussian random field | sums | EXTREMES | CONVERGENCE | STATISTICS & PROBABILITY | STATIONARY-SEQUENCES | RANDOM-VARIABLES | Gaussian distribution | Time dependence | Fields (mathematics) | Normal distribution
Journal Article
Annals of Probability, ISSN 0091-1798, 03/2017, Volume 45, Issue 2, pp. 1160 - 1189
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this... 
Gaussian process | Excursion set | Large deviations | Topology | Exceedence probabilities | large deviations | STATISTICS & PROBABILITY | exceedence probabilities | excursion set | topology
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 12/2015, Volume 125, Issue 12, pp. 4473 - 4488
Mass-stationarity means that the origin is at a typical location in the mass of a random measure. It is an intrinsic characterization of Palm versions with... 
Stationary random measure | Allocation | Point process | Invariant transport | Palm measure | Mass-stationarity | Preserving shift | MSC primary 60G57 | 60G55 | secondary 60G60
Journal Article
Potential Analysis, ISSN 0926-2601, 10/2018, Volume 49, Issue 3, pp. 359 - 379
We consider the family of finite signed measures on the complex plane ℂ $\mathbb {C}$ with compact support, of finite logarithmic energy and with zero total... 
Geometry | Markov property | Potential Theory | Functional Analysis | Logarithmic energy | Beppo Levi space | Gaussian field | Probability Theory and Stochastic Processes | Mathematics | Logarithmic potential | Primary 31A15 | Secondary 60G60, 31C25 | MATHEMATICS
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 04/2015, Volume 125, Issue 4, pp. 1605 - 1628
We consider the stochastic wave equation on the real line driven by space–time white noise and with irregular initial data. We give bounds on higher moments... 
Nonlinear stochastic wave equation | Hyperbolic Anderson model | Intermittency | Growth indices | Secondary | Primary | 35R60 | secondary 60G60 | MSC: primary 60H15 | EXISTENCE | SMOOTHNESS | STATISTICS & PROBABILITY | VALUES
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 07/2013, Volume 31, Issue 4, pp. 708 - 736
We prove the existence of a stochastic flow of Hölder homeomorphisms for solutions of SDEs with singular time dependent drift having only certain integrability... 
Stochastic differential equations | Secondary 60G60, 60J65, 35K10 | Singular drift | Weak differentiability | Primary 60H10 | Flow | Strong solutions | 60J65 | EXISTENCE | MATHEMATICS, APPLIED | Secondary 60G60 | STATISTICS & PROBABILITY | 35K10 | UNIQUENESS | STOCHASTIC-EQUATIONS | Drift | Stochasticity | Probability | Mathematics
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 4/2017, Volume 23, Issue 2, pp. 288 - 323
Journal Article
Advances in Applied Probability, ISSN 0001-8678, 06/2015, Volume 47, Issue 2, pp. 307 - 327
Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function... 
60D05 | Celestial body | simulation of star-shaped random set | fractal dimension | 60G60 | random field on a sphere | 37F35 | correlation function | Lévy basis
Journal Article
Stochastic Partial Differential Equations: Analysis and Computations, ISSN 2194-0401, 9/2015, Volume 3, Issue 3, pp. 360 - 397
Journal Article
Stochastic Partial Differential Equations: Analysis and Computations, ISSN 2194-0401, 9/2014, Volume 2, Issue 3, pp. 316 - 352
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 05/2013, Volume 31, Issue 3, pp. 359 - 380
Journal Article
Stochastic Models, ISSN 1532-6349, 04/2013, Volume 29, Issue 2, pp. 273 - 289
In many applications related with geostatistics, biological and medical imaging, material science, and engineering surfaces, the real observations have... 
Skew Student's t random field | Primary 60D05 | Secondary 60G60, 52A22 | Expected Euler-Poincaré characteristic | Excursion sets | Skewness | Surface roughness | Lipschitz-Killing curvatures | DISTRIBUTIONS | Expected Euler-Poincare characteristic | 52A22 | SCALE MIXTURES | Secondary 60G60 | STATISTICS & PROBABILITY
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 06/2010, Volume 28, Issue 4, pp. 662 - 695
We study nonlinear heat and wave equations on a Lie group. The noise is assumed to be a spatially homogeneous Wiener process. We give necessary and sufficient... 
Stochastic heat and wave equations | Homogeneous Wiener process | Secondary 60G60, 35K05, 35L05 | Primary 60H15 | Stochastic evolution on a Lie group | SPACE | DIMENSIONS | MATHEMATICS, APPLIED | REGULARITY | PARTIAL-DIFFERENTIAL EQUATIONS | STATISTICS & PROBABILITY | Kernels | Covariance | Noise | Lie groups | Wave equations | Nonlinearity | Stochasticity
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 11/2008, Volume 142, Issue 3, pp. 443 - 473
Journal Article
by Hu, Y
Applied Mathematics and Optimization, ISSN 0095-4616, 1/2001, Volume 43, Issue 3, pp. 221 - 243
This paper is concerned with the following stochastic heat equations: $$\frac{{\partial u_t (x)}} {{\partial t}} = \frac{1} {2}\Delta u_t (x) + w^H \cdot u_t... 
Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Numerical and Computational Physics | Heat equations, Fractional Brownian field, Multiple integral of Itô type | Mathematics | Stochastic integral of Itô type, Chaos expansion, Asymptotic behavior, Mittag—Leffler function. AMS Classification. Primary 60H15, 60H05, Secondary 60G60, 35K05, 35R60, 60F25 | Heat equations, Fractional Brownian field, Multiple integral of Itô type, Stochastic integral of Itô type, Chaos expansion, Asymptotic behavior, Mittag—Leffler function. AMS Classification. Primary 60H15, 60H05, Secondary 60G60, 35K05, 35R60, 60F25 | Chaos expansion | Multiple integral of Itô type | Stochastic integral of Itô type | Mittag-Leffler function | Asymptotic behavior | Fractional Brownian field | Heat equations | BROWNIAN-MOTION | INTEGRALS | fractional Brownian field | MATHEMATICS, APPLIED | asymptotic behavior | chaos expansion | heat equations | multiple integral of Ito type | PARTIAL-DIFFERENTIAL EQUATIONS | stochastic integral of Ito type | Time dependence | Parameters | Exponents | Noise | Mathematical analysis | White noise | Texts | HEAT | MATHEMATICAL SOLUTIONS | DISTRIBUTION | MATHEMATICAL SPACE | STOCHASTIC PROCESSES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS | NOISE | POTENTIALS | TIME DEPENDENCE | CHAOS THEORY | LYAPUNOV METHOD
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 08/2000, Volume 117, Issue 4, pp. 551 - 587
Journal Article
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