Results 51 to 60 of about 2,363 (94)
Generalized functionals of Brownian motion
International Journal of Stochastic Analysis, Volume 7, Issue 3, Page 247-267, 1994., 1993 In this paper we discuss some recent developments in the theory of generalized functionals of Brownian motion. First we give a brief summary of the Wiener‐Ito multiple Integrals. We discuss some of their basic properties, and related functional analysis on Wiener measure space. then we discuss the generalized functionals constructed by Hida.
N. U. Ahmed
wiley +1 more source
Pseudo S-asymptotically Bloch type periodicity with applications to partial stochastic neutral evolution equations [PDF]
Arab Journal of Mathematical SciencesPurposeThis paper introduces the concept of (µ, ν)-pseudo S-asymptotically Bloch type (ω, k)- periodic functions, aiming to extend the framework of periodicity in stochastic analysis and to investigate their role in neutral partial stochastic ...
Marwa Missaoui
doaj +1 more source
Well-posedness of the stochastic transport equation with unbounded drift
, 2017 The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained.
Mollinedo, David A. C. +1 more
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A Differentiation Theory for It\^o's Calculus
, 2010 A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus.
Bhattacharya R. +3 more
core +1 more source
On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise
Advances in Nonlinear Analysis, 2017 In this article, we deal with the stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasis is on analyzing the effects of a multiplicative Lévy noise on such problems and on establishing a well ...
Biswas Imran H. +2 more
doaj +1 more source
A note on intermittency for the fractional heat equation [PDF]
, 2013 The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-\Delta)^{\beta/2} u(t,x) + u(t,x)\dot{W}(t,x), \quad t>0,x \in \bR^d$$ with initial condition ...
Balan, Raluca, Conus, Daniel
core +1 more source
Absolute continuity for SPDEs with irregular fundamental solution
, 2014 For the class of stochastic partial differential equations studied in [Conus-Dalang,2008], we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space.
Sanz-Solé, Marta, Süß, André
core +1 more source
Stochastic stability and instability of rumor model
Open MathematicsIn this study, we present a stochastic rumor model. The stability of the disease-free equilibrium state and instability of the free equilibrium E0{E}_{0} of stochastic epidemics model are considered with the help of Lyapunov functions.
Zhang Jing, Wang Xinyao, Wang Xiaohuan
doaj +1 more source
Exponential mixing for some SPDEs with L\'evy noise
, 2010 We show how gradient estimates for transition semigroups can be used to establish exponential mixing for a class of Markov processes in infinite dimensions. We concentrate on semilinear systems driven by cylindrical $\alpha$-stable noises, $\alpha \in (0,
Priola, Enrico, Xu, Lihu, Zabczyk, Jerzy
core +1 more source
Decorrelation of total mass via energy [PDF]
, 2014 The main result of this small note is a quantified version of the assertion that if u and v solve two nonlinear stochastic heat equations, and if the mutual energy between the initial states of the two stochastic PDEs is small, then the total masses of ...
Chen, Le +2 more
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