53 research outputs found
Fractional backward stochastic differential euqations and fractional backward variational inequalities
In the framework of fractional stochastic calculus, we study the existence
and the uniqueness of the solution for a backward stochastic differential
equation, formally written as: [{[c]{l}% -dY(t)=
f(t,\eta(t),Y(t),Z(t))dt-Z(t)\delta B^{H}(t), \quad t\in[0,T], Y(T)=\xi,.]
where is a stochastic process given by , , and is a
fractional Brownian motion with Hurst parameter greater than 1/2. The
stochastic integral used in above equation is the divergence-type integral.
Based on Hu and Peng's paper, \textit{BDSEs driven by fBm}, SIAM J Control
Optim. (2009), we develop a rigorous approach for this equation. Moreover, we
study the existence of the solution for the multivalued backward stochastic
differential equation [{[c]{l} -dY(t)+\partial\varphi(Y(t))dt\ni
f(t,\eta(t),Y(t),Z(t))dt-Z(t)\delta B^{H}(t),\quad t\in[0,T], Y(T)=\xi,.] where
is a multivalued operator of subdifferential type associated
with the convex function .Comment: 41 page
Kinematic reduction of reaction-diffusion fronts with multiplicative noise: Derivation of stochastic sharp-interface equations
We study the dynamics of generic reaction-diffusion fronts, including pulses
and chemical waves, in the presence of multiplicative noise. We discuss the
connection between the reaction-diffusion Langevin-like field equations and the
kinematic (eikonal) description in terms of a stochastic moving-boundary or
sharp-interface approximation. We find that the effective noise is additive and
we relate its strength to the noise parameters in the original field equations,
to first order in noise strength, but including a partial resummation to all
orders which captures the singular dependence on the microscopic cutoff
associated to the spatial correlation of the noise. This dependence is
essential for a quantitative and qualitative understanding of fluctuating
fronts, affecting both scaling properties and nonuniversal quantities. Our
results predict phenomena such as the shift of the transition point between the
pushed and pulled regimes of front propagation, in terms of the noise
parameters, and the corresponding transition to a non-KPZ universality class.
We assess the quantitative validity of the results in several examples
including equilibrium fluctuations, kinetic roughening, and the noise-induced
pushed-pulled transition, which is predicted and observed for the first time.
The analytical predictions are successfully tested against rigorous results and
show excellent agreement with numerical simulations of reaction-diffusion field
equations with multiplicative noise.Comment: 17 pages, 6 figure
Rapid evolution of coordinated and collective movement in response to artificial selection.
Collective motion occurs when individuals use social interaction rules to respond to the movements and positions of their neighbors. How readily these social decisions are shaped by selection remains unknown. Through artificial selection on fish (guppies, Poecilia reticulata) for increased group polarization, we demonstrate rapid evolution in how individuals use social interaction rules. Within only three generations, groups of polarization-selected females showed a 15% increase in polarization, coupled with increased cohesiveness, compared to fish from control lines. Although lines did not differ in their physical swimming ability or exploratory behavior, polarization-selected fish adopted faster speeds, particularly in social contexts, and showed stronger alignment and attraction responses to multiple neighbors. Our results reveal the social interaction rules that change when collective behavior evolves
Stochastic evolution equations driven by Liouville fractional Brownian motion
Let H be a Hilbert space and E a Banach space. We set up a theory of
stochastic integration of L(H,E)-valued functions with respect to H-cylindrical
Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in
the interval (0,1). For Hurst parameters in (0,1/2) we show that a function
F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical
Liouville fBm if and only if it is stochastically integrable with respect to an
H-cylindrical fBm with the same Hurst parameter. As an application we show that
second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by
space-time noise which is white in space and Liouville fractional in time with
Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous
both and space.Comment: To appear in Czech. Math.
Cylindrical fractional Brownian motion in Banach spaces
In this article we introduce cylindrical fractional Brownian motions in Banach spaces and develop the related stochastic integration theory. Here a cylindrical fractional Brownian motion is understood in the classical framework of cylindrical random variables and cylindrical measures. The developed stochastic integral for deterministic operator valued integrands is based on a series representation of the cylindrical fractional Brownian motion, which is analogous to the Karhunen-Loève expansion for genuine stochastic processes. In the last part we apply our results to study the abstract stochastic Cauchy problem in a Banach space driven by cylindrical fractional Brownian motion
National cultural autonomy and linguistic rights in Central and Eastern Europe
The theory and practice of national cultural autonomy (NCA) are examined from the perspective of national minorities’ linguistic rights in four countries of Central and Eastern Europe (CEE): Hungary, Estonia, Serbia and Russia. The idea of NCA dates back to the end of the nineteenth century and is based on the principle of ethnic communities’ autonomy—within a multi-ethnic state—to manage their own linguistic and cultural affairs. The notion of NCA was rediscovered in the 1990s and incorporated into the law and practice of the said four countries. Using a comparative approach, the chapter reflects upon NCA’s potential contribution in advancing the linguistic rights of national minorities in CEE. It concludes that, while the actual autonomy afforded to minority institutions in CEE is often restricted, NCA may serve as a platform to articulate concerns of great salience to national minorities, encompassing minority participation and multilingual education
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