Nonlinear stochastic wave and heat equations

By S. Peszat, Jerzy Zabczyk. 2000

178 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a47c183156fe2fc8ab78554de10e205261292bd

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Citations in the corpus

Stochastic evolution equations with fractional Brownian motion (2003, unknown): “This condition is equivalent to conditions presented in work done in [20] for both the stochastic heat and wave equations in Euclidean space Rd with d ≥ 2; therein, the authors even treat non-linear equations under a non-degeneracy assumption on the nonlinearity function F (F bounded above and below”
Strong solutions to stochastic wave equations with values in Riemannian manifolds (2007, background): “Remark 4.1. The reader is referred to [41] and [ 42 ] for further details on spatially homogeneous Wiener process.”
Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise (2003, background): “These results have been extended to higher dimensions and to a wider class of equations by many authors [17], [6], [22], [23], [3], [7], [15], [16], [21].”
Non-linear rough heat equations (2009, methodology): “Perhaps this hypothesis could be retrieved by working with weighted L p-spaces, as in [39].”
On the existence and position of the farthest peaks of a family of stochastic heat and wave equations (2010, background): “Moreover, under various conditions on σ ,( 1.2) is necessary for the existence of a solution [10, 26 ].”
Equivalence and Hölder-Sobolev regularity of solutions for a class of non-autonomous stochastic partial differential equations (2003, background): “Moreover, following [50] , several notions of mild solutions that involve Green's functions, Green's distributions or more general semi-group arguments have been used to investigate the existence and the regularity properties of solutions to several classes of hyperbolic and parabolic stochastic par”
Asymptotics of solutions to semilinear stochastic wave equations (2006, background): “For some related works on stochastic wave equations, we mention the interesting papers [17, 20, 21], among many others.”
Stochastic Heat Equation with Multiplicative Fractional-Colored Noise (2008, background): “Other related references are: [36], [23], [33], [11] and [12].”
On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients (2005, background): “chitz continuous in u.A suﬃcient condition for strong existence and uniqueness of solutions is given by (A)η for η≤ 1, see Dalang [Dal99] (see also Theorem 6.1 in the Appendix) and Peszat and Zabczyk [PZ00]. H¨older continuity of the sample paths was established by Sanz-Sol´e and Sarr`a [SSS02] if η”
Intermittence and nonlinear parabolic stochastic partial differential equations (2008, methodology): “See also Da Prato [12] and Da Prato and Zabczyk [13].”
Stochastic integrals for spde's: a comparison (2010, methodology): “4, we discuss the Hilbert-space-valued approach to the study of the same equations, using the approach of [32].”
Malliavin Calculus with Applications to Stochastic Partial Differential Equations (2005, background): “A different approach to SPDE’s driven by coloured noise and the study of the required stochastic integrals is given in reference [53] (see also the references therein), following mainly the theoretical basis from reference [16].”