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Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence
Springer Science and Business Media LLC - Tập 4 - Trang 791-826 - 2016
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process ...... hiện toàn bộ
Convergence of the Finite Volume method for scalar conservation laws with multiplicative noise: an approach by kinetic formulation
Springer Science and Business Media LLC - Tập 8 - Trang 265-310 - 2019
Under a standard CFL condition, we prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported noise. In Dotti and Vovelle (Arch Ration Mech Anal 230(2):539–591, 2018), a framework for the analysis of the convergence of approximations to stochastic scalar first-order c...... hiện toàn bộ
Convergence of tamed Euler schemes for a class of stochastic evolution equations
Springer Science and Business Media LLC - Tập 4 - Trang 225-245 - 2015
We prove stability and convergence of a full discretization for a class of stochastic evolution equations with super-linearly growing operators appearing in the drift term. This is done by using the recently developed tamed Euler method, which employs a fully explicit time stepping, coupled with a Galerkin scheme for the spatial discretization.
Vortices in a stochastic parabolic Ginzburg-Landau equation
Springer Science and Business Media LLC - Tập 5 - Trang 113-143 - 2016
We consider the variant of a stochastic parabolic Ginzburg-Landau equation that allows for the formation of point defects of the solution. The noise in the equation is multiplicative of the gradient type. We show that the family of the Jacobians associated to the solution is tight on a suitable space of measures. Our main result is the characterization of the limit points of this family. They are ...... hiện toàn bộ
Stochastic integration and stochastic PDEs driven by jumps on the dual of a nuclear space
Springer Science and Business Media LLC - Tập 6 - Trang 618-689 - 2018
We develop a novel theory of weak and strong stochastic integration for cylindrical martingale-valued measures taking values in the dual of a nuclear space. This is applied to develop a theory of SPDEs with rather general coefficients. In particular, we can then study SPDEs driven by general Lévy processes in this context.
$$L^p$$ -estimates and regularity for SPDEs with monotone semilinearity
Springer Science and Business Media LLC - - 2019
Semilinear stochastic partial differential equations on bounded domains $${\mathscr {D}}$$ are considered. The semilinear term may have arbitrary polynomial growth as long as it is continuous and monotone except perhaps near the origin. Typical examples are the stochastic Allen–Cahn and Ginzburg–Landau equations. The first main result of this article are $$L^p$$-estimates for such equations. The $...... hiện toàn bộ
Inviscid limit for stochastic second-grade fluid equations
Springer Science and Business Media LLC - - Trang 1-54 - 2023
We consider in a smooth bounded and simply connected two dimensional domain the convergence in the
$$L^2$$
norm, uniformly in time, of the solution of the stochastic second-grade fluid equations with transport noise and no-slip boundary conditions to the solution of the corresponding Euler equations. We prove...... hiện toàn bộ
Absolute continuity of the solution to stochastic generalized Burgers–Huxley equation
Springer Science and Business Media LLC - - Trang 1-61 - 2023
The present work deals with the global solvability as well as absolute continuity of the law of the solution to stochastic generalized Burgers–Huxley (SGBH) equation driven by multiplicative space-time white noise in a bounded interval of
$${\mathbb {R}}$$
. We first prove the existence of a unique local mild ...... hiện toàn bộ
Feynman–Kac formula for perturbations of order $$\le 1$$, and noncommutative geometryAbstract Let Q be a differential operator of order $$\le 1$$
≤
1
$$\mathscr {E}\rightarrow \mathscr {M}$$
E
→
M
$$\nabla $$
∇
$$\mathscr {M}$$
M
Q that guarantee that $$\nabla ^{\dagger }\nabla /2+Q$$
∇
†
∇
/
2
+
Q
$$\mathrm {e}^{-zH^{\nabla }_{Q}}$$
e
-
z
H
Q
∇
$$\Gamma _{L^2}(\mathscr {M},\mathscr {E})$$
Γ
L
2
(
M
,
E
)
z runs through a complex sector which contains $$[0,\infty )$$
[
0
,
∞
)
$$\mathrm {e}^{-tH^{\nabla }_{Q}}$$
e
-
t
H
Q
∇
$$t>0$$
t
>
0
Q is a self-adjoint zeroth order operator. For compact $$\mathscr {M}$$
M
$$\begin{aligned} \mathrm {Tr}\left( \widetilde{V}\int ^t_0\mathrm {e}^{-sH^{\nabla }_{V}}P\mathrm {e}^{-(t-s)H^{\nabla }_{V}}\mathrm {d}s\right) , \end{aligned}$$
Tr
V
~
∫
0
t
e
-
s
H
V
∇
P
e
-
(
t
-
s
)
H
V
∇
d
s
,
$$V,\widetilde{V}$$ hiện toàn bộ
Springer Science and Business Media LLC - - 2023
On $$L_{p}$$ - theory for stochastic parabolic integro-differential equations
Springer Science and Business Media LLC - - 2013
The existence and uniqueness in fractional Sobolev spaces of the Cauchy problem to a stochastic parabolic integro-differential equation is investigated. A model problem with coefficients independent of space variable is considered. The equation arises in a filtering problem with a jump signal and jump observation process.
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